Inclusion Criteria:

          -  Acute myeloid leukemia with a FLT3-internal tandem duplication (ITD) who are in a
             complete remission or partial remission (less than 10% blasts in marrow) as documented
             by bone marrow biopsy and who plan to undergo a bone marrow transplantation

          -  Patients who have had count recovery (absolute neutrophil count [ANC] > 500,000/mm^3;
             non transfused platelet count over 30,000/mm^3) and are at least 30 days after
             induction and/or transplantation but no more than 120 days post transplant

          -  Patients may have received any prior therapy deemed necessary for induction of
             remission except for patients whom have progressed while on sorafenib; patients who
             have responded to sorafenib previously are eligible for enrollment on the protocol

          -  Eastern Cooperative Oncology Group (ECOG) performance status =< 2 (Karnofsky >= 60%)

          -  Life expectancy of greater than four months

          -  Total bilirubin less than 2 x upper limit of normal

          -  Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase
             [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT])
             =< 5 x institutional upper limit of normal

          -  Creatinine =< 1.5 x upper limit of normal OR creatinine clearance >= 60 mL/min/1.73
             m^2 for patients with creatinine levels > 1.5 x upper limit of normal

          -  The effects of sorafenib on the developing human fetus are unknown; for this reason
             and because tyrosine kinase inhibiting agents are known to be teratogenic, 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 and for the duration
             of study participation; should a woman become pregnant or suspect she is pregnant
             while participating in this study, she should inform her treating physician
             immediately; contraception should continue for at least 30 days after the last dose of
             sorafenib

          -  Ability to understand and the willingness to sign a written informed consent document

        Exclusion Criteria:

          -  Patients who have had chemotherapy or radiotherapy within 2 weeks except for
             intrathecal chemotherapy (i.e., methotrexate, cytarabine, or thiotepa)

          -  Patients may not be receiving any other investigational agents

          -  Patients with uncontrolled hypertension (i.e., persistent grade 3 while undergoing
             treatment)

          -  History of allergic reactions attributed to compounds of similar chemical or biologic
             composition to sorafenib

          -  Patients with active and/or untreated central nervous system (CNS) leukemia will not
             be eligible

          -  Patients must not have any evidence of bleeding diathesis or be on any therapeutic
             anticoagulation such as low molecular weight (LMW) heparin or warfarin for deep vein
             thrombosis (DVT) treatment

          -  Uncontrolled intercurrent illness including, but not limited to ongoing or active
             infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac
             arrhythmia, or psychiatric illness/social situations that would limit compliance with
             study requirements

          -  Pregnant women are excluded from this study because sorafenib is chemotherapeutic
             agent with the potential for teratogenic or abortifacient effects; because there is an
             unknown but potential risk for adverse events in nursing infants secondary to
             treatment of the mother with sorafenib, breastfeeding should be discontinued if the
             mother is treated sorafenib

          -  Human immunodeficiency virus (HIV)-positive patients are excluded because management
             of these patients in the hematopoietic cell transplant setting has not yet been well
             defined and is currently the subject of investigation in other studies addressing this
             issue

          -  Patients with active acute GVHD who have been initiated on therapy or had therapy
             escalation within 21 days are not eligible

          -  Patients with lack of engraftment (less than 90% donor deoxyribonucleic acid [DNA] in
             bone marrow or peripheral blood) after bone marrow transplant as evidence by RFLP
             (restriction fragment length polymorphism) are not eligible

          -  Patients who are unable to swallow pills are not eligible

          -  Patients taking strong cytochrome P450 family 3, subfamily A, polypeptide 4 (CYP3A4)
             inhibitors including enzyme-inducing anti-epileptic drugs (phenytoin, carbamazepine,
             or phenobarbital), rifampin, grape fruit juice, or St. John's wort are not eligible