Inclusion Criteria:

- Patients must be ≥ 18 years old at the time of enrollment and have a documented germline NF1 mutation in a CLIA certified laboratory or a diagnosis of NF1 based on clinical NIH consensus criteria. In addition to substantial cutaneous neurofibroma burden as defined below, at least one of the criteria below have to be present:

- Six or more café-au-lait macules (≥0.5cm in prepubertal subjects or ≥1.5 cm in post pubertal subjects)

- Freckling in axilla or groin

- Optic glioma

- Two or more Lisch nodules

- A distinctive bony lesion (dysplasia of the sphenoid bone or dysplasia or thinning of long bone cortex)

- A first-degree relative with NF1

- Histologic confirmation of tumor is not necessary in the presence of consistent clinical findings.

- Measurable disease: Patients must have substantial cutaneous neurofibroma burden causing distress to the patient by disfigurement or itching. Patients must have ≥ 9 measurable cutaneous neurofibromas. For the purpose of this study measurability will be defined for each of the lesions selected as target lesions as a neurofibroma with a longest diameter ≥ 3 mm in the longest diameter.

- ECOG performance status <2

- Patients must have normal organ and marrow function as defined below:

- hemoglobin >10 g/dL (not requiring RBC transfusions)

- absolute neutrophil count >1,500/mcL

- platelets >100,000/mcL (not requiring platelet transfusions)

- total bilirubin < 1.5 X upper limit of normal (ULN), with the exception of patients with Gilbert Syndrome who are required to have < 3 X ULN

- ALT(SGPT) <3.0 X ULN

- creatinine within normal institutional limits OR

- creatinine clearance >60 mL/min/1.73 m2 for patients with creatinine levels above institutional normal

- Hematologic parameters for patients undergoing biopsy only: Patients should have INR <1.4 and PT ≤ 40 seconds (unless due to lupus anticoagulant). In patients not meeting these parameters, clearance by hematology will be required prior to undergoing a biopsy.

- Ability of subject or Legally Authorized Representative (LAR) to understand and the willingness to sign a written informed consent document.

- Willingness to avoid excessive sun exposure and use adequate sunscreen protection if sun exposure is anticipated.

- Willingness to avoid the ingestion of grapefruit and Seville oranges (as well as other products containing these fruits, e.g. grapefruit juice or marmalade) during the study.

- Prior therapy:

- Since there is no standard effective chemotherapy for patients with NF1 and cutaneous neurofibromas, patients may be treated on this trial without having received prior medical therapy directed at their PN.

- Since selumetinib is not expected to cause substantial myelosuppression, there will be no limit to number of prior myelosuppressive regimens previously received for NF1 related or other tumor manifestations.

- Patients who have received previous investigational agents or biologic therapy, such as tipifarnib, pirfenidone, Peg-Intron, sorafenib, or other VEGFR inhibitors are eligible for enrollment.

- Growth factors that support platelet or white cell number or function must not have been administered within the past 7 days and are not permitted while on the study.

- At least 6 weeks must have elapsed prior to enrollment since the patient received any prior radiation therapy, and the target cutaneous neurofibromas have to be in areas outside of a prior radiation field.

- At least 4 weeks must have elapsed since receiving medical therapy directed at NF1 related tumor manifestations.

- At least 4 weeks must have elapsed since any surgeries, with evidence of completed wound healing.

- Patients who received prior medical therapy for a NF1 related tumor must have recovered from the acute toxic effects of all prior therapy to ≤ grade 1 CTCAE version 4.0 before entering this study.

- The effects of selumetinib on the developing human fetus at the recommended therapeutic dose are unknown. For this reason women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 4 weeks after dosing with selumetinib ceases. Women of child-bearing potential must have a negative pregnancy test prior to entry. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, the patient should inform her treating physician immediately. Please note that the selumetinib manufacturer recommends that adequate contraception for male patients should be used for 12 weeks post-last dose due to sperm life cycle.

- Informed Consent: Diagnostic or laboratory studies performed exclusively to determine eligibility for this trial must only be done after obtaining written informed consent from all patients, which can be accomplished using the study specific informed consent or another consent, such as the NCI, POB screening protocol. Studies or procedures that were performed for clinical indications (not exclusively to determine eligibility) may be used for screening or baseline values even if the studies were done before informed consent was obtained, if the patient agrees.

Exclusion Criteria:

- Patients who are receiving any other investigational agents, or have received an investigational agent within the past 30 days.

- May not have a NF1 related tumor such as optic pathway glioma or malignant peripheral nerve sheath tumor, which requires treatment with chemotherapy, radiation, or surgery.

- Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, active bleeding diatheses or renal transplant, including any patient known to have hepatitis B, hepatitis C or human immunodeficiency virus (HIV), or psychiatric illness/social situations that would limit compliance with study requirements. Patients with HIV who have adequate CD4 counts and who have no requirement for antiviral therapy will be eligible.

- Pregnant or breast-feeding females are excluded due to potential risks of fetal and teratogenic adverse events of an investigational agent. Males or females of reproductive potential may not participate unless they have agreed to use an effective contraceptive method. Abstinence is an acceptable method of birth control.

- Prior treatment with selumetinib or another specific MEK 1/2 inhibitor.

- No supplementation with vitamin E is permitted.

- Inability to swallow capsules, since capsules cannot be crushed or broken.

- Refractory nausea and vomiting, chronic gastrointestinal diseases (e.g., inflammatory bowel disease), or significant bowel resection that would preclude adequate absorption.

- Strong inhibitors or inducers of hepatic microsomal isoenzymes

- While not an exclusion criterion, unless clinically indicated, patients should avoid taking other additional non-study medications that may interfere with the study medications. In particular, patients should avoid medications that are known to be strong inhibitors or inducers of hepatic microsomal isoenzymes CYP1A2, CYP2C8, CYP2C9, CYP2C19, CYP3A4/5, UGT1A1, UGT1A3 and transporters BCRP and P-gp. Because the lists of these agents are constantly changing, it is important to regularly consult a frequently-updated medical reference. As part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter medicine or herbal product.

- Known Cardiac Disorder, including:

- Uncontrolled hypertension (blood pressure [BP] of ≥150/95 despite medical support/management)

- Acute coronary syndrome within 6 months prior to starting treatment

- Uncontrolled angina - Canadian Cardiovascular Society grade II-IV despite medical support/management

- Heart failure NYHA Class II or above (for the NYHA Classification refer to Appendix II)

- Prior or current cardiomyopathy including but not limited to the following: known hypertrophic cardiomyopathy

- Known arrhythmogenic right ventricular cardiomyopathy

- Baseline left ventricular ejection fraction (LVEF) ≤ 55%

- Previous moderate or severe impairment of left ventricular systolic function (LVEF <45% on echocardiography or equivalent on Multi-Gated Acquisition Scan [MUGA]) even if full recovery has occurred.

- Severe valvular heart disease

- Atrial fibrillation with a ventricular rate >100 bpm on ECG at rest

- QTcF interval >450 msec or other factors that increase the risk of QT prolongation or arrhythmic events (e.g., heart failure, hypokalemia, family history of long QT interval syndrome) are excluded. The use of medication(s) that can prolong QTc interval is prohibited while treated on this study. For a comprehensive list of agents that prolong QTc refer to a frequently-updated medical reference, such as https://www.crediblemeds.org/everyone/composite-list-all-qtdrugs.

- Known Ophthalmologic conditions, such as:

- Current or past history of retinal pigment epithelial detachment (RPED)/central serous retinopathy (CSR)

- Current or past history of retinal vein occlusion

- Known intraocular pressure (IOP) > 21 mmHg (or ULN adjusted by age) or uncontrolled glaucoma (irrespective of IOP); patients with controlled glaucoma and increased IOP who do not have meaningful vision (light perception only or no light perception) may be eligible after discussion with the study chair.

- Subjects with any other significant abnormality on ophthalmic examination (performed by an ophthalmologist) should be discussed with the Study Chair for potential eligibility

- Ophthalmological findings secondary to long-standing optic pathway glioma (such as visual loss, optic nerve pallor or strabismus) or long-standing orbito-temporal PN (such as visual loss, strabismus) will NOT be considered a significant abnormality for the purposes of the study

- Known severe hypersensitivity to selumetinib or any excipient of selumetinib or history of allergic reactions attributed to compounds of similar chemical or biologic composition to selumetinib

- Have had recent major surgery within a minimum of 4 weeks prior to starting study treatment, with the exception of surgical placement for vascular access.

- Have any unresolved chronic toxicity with CTC AE grade ≥ 2, from previous anti-NF1 therapy, except for alopecia.

- Clinical judgment by the investigator that the patient should not participate in the study