Inclusion Criteria:

          -  Patient willing and able to provide written informed consent for the trial.

          -  Patient age ≥ 18 at time of consent.

          -  Histologically or cytologically confirmed malignant pleural or peritoneal mesothelioma
             (MPM).

          -  No plans for surgical resection.

          -  At least one prior line of systemic therapy. Note: Patients on prior immunotherapy are
             eligible.

          -  At least one targetable lesion appropriate for palliative SBRT and one non-target
             lesion

          -  Karnofsky Performance Score (KPS) ≥ 70%

          -  If of childbearing potential, must be willing to use highly effective mode of
             contraception for at least one month prior, during, and for 2 months after the end of
             active therapy

          -  Adequate organ function, defined as:

               -  Absolute Neutrophil Count ≥ 1.5K/mcL.

               -  Platelet count ≥ 100K/mcL.

               -  Adequate renal function as defined by an estimated creatinine clearance ≥ 30
                  mL/min according to the Cockcroft-Gault formula or serum creatinine ≤ 1.5 x ULN

               -  Hemoglobin > 9g/dL (prior transfusion permitted)

               -  Total bilirubin level ≤ 1.5 × the upper limit of normal (ULN) range

               -  AST and ALT levels ≤ 2.5 × ULN or AST and ALT levels ≤ 5 x ULN (for subjects with
                  documented metastatic disease to the liver).

          -  If the patient received major surgery, they must have recovered adequately from the
             toxicity and/or complications from the intervention prior to starting therapy.

        Exclusion Criteria:

          -  Currently participating and receiving another study therapy or has participated in a
             study of an investigational agent and received study therapy or used an
             investigational device within 4 weeks of the first dose of treatment.

          -  Prior radiation therapy precluding SBRT

          -  Continuous oxygen use

          -  Current use of immunosuppressive medication, EXCEPT for the following: a. intranasal,
             inhaled, topical steroids, or local steroid injection (e.g., intra-articular
             injection); b. Systemic corticosteroids at physiologic doses ≤ 10 mg/day of prednisone
             or equivalent; c. Steroids as premedication for hypersensitivity reactions (e.g., CT
             scan premedication).

          -  Active autoimmune disease that might deteriorate when receiving an immunostimulatory
             agent. Patients with diabetes type I, vitiligo, psoriasis, or hypo- or hyperthyroid
             diseases not requiring immunosuppressive treatment are eligible. Replacement therapy
             (e.g. thyroxine, insulin, or physiologic corticosteroid replacement therapy for
             adrenal or pituitary insufficiency) is not considered a form of systemic treatment.

          -  Known prior severe hypersensitivity to investigational product or any component in its
             formulations, including known severe hypersensitivity reactions to monoclonal
             antibodies (NCI CTCAE v4.03 Grade ≥ 3)

          -  Patient who rapidly progressed on prior immunotherapy, as determined by the treating
             physician, are not eligible.

          -  Prior Therapies:

               1. Treatment with a monoclonal antibody within 4 weeks prior to study Day 1 or has
                  not recovered (i.e., ≥ Grade 1 at baseline) from adverse events due to agents
                  administered

               2. Prior chemotherapy, targeted small molecule therapy, within 4 weeks prior to
                  study Day 1 or has not recovered (i.e., ≥ Grade 1 at baseline) from adverse
                  events due to a previously administered agent (excluding Grade 2 neuropathy).

               3. Prior therapy with an anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CD137, or anti-
                  Cytotoxic T-lymphocyte-associated antigen-4 (CTLA-4) antibody (including
                  ipilimumab or any other antibody or drug specifically targeting T-cell
                  co-stimulation or checkpoint pathways) within 4 weeks prior to study Day 1 or has
                  not recovered (i.e., >/= Grade 1 at baseline) from adverse events

          -  Comorbidities or Prior Conditions:

               1. Known psychiatric or substance abuse disorders that would interfere with
                  cooperation with the requirements of the trial.

               2. Prior organ transplantation including allogenic stem-cell transplantation.

               3. Known additional malignancy that is progressing or requires active treatment.
                  Exceptions include basal cell carcinoma of the skin, squamous cell carcinoma of
                  the skin, or in situ cervical cancer that has undergone potentially curative
                  therapy.

               4. Known history of active TB (Tuberculosis).

               5. Known history of HIV or known acquired immunodeficiency syndrome.

               6. Active Hepatitis B virus (HBV) or Hepatitis C virus (HCV) infection at screening
                  or positive serologies indicating prior infection.

               7. Active infection requiring systemic therapy.

               8. Evidence of interstitial lung disease or active, non-infectious pneumonitis.

               9. Clinically significant (i.e., active) cardiovascular disease: cerebral vascular
                  accident/stroke (< 6 months prior to enrollment), myocardial infarction (< 6
                  months prior to enrollment), unstable angina, congestive heart failure (≥ New
                  York Heart Association Classification Class II), or serious cardiac arrhythmia
                  requiring medication.

          -  Pregnant women or women who are breastfeeding or of childbearing potential and not
             using a highly effective method of birth control for at least one month prior to
             enrollment. If the risk of contraception exists, male and female subjects must use
             highly effective contraception throughout the study and for at least 60 days after
             last avelumab treatment.

             a. Highly effective contraception includes either 2 barrier methods (diaphragm, condom
             by the partner, copper intrauterine device, sponge, or spermicide), or 1 barrier
             method and 1 hormonal method (any oral, subcutaneous, intrauterine, or intramuscular
             registered and marketed contraceptive agent that contains an estrogen and/or a
             progesterone agent).

          -  Vaccination within 4 weeks prior to the first dose of avelumab and while on trial is
             prohibited except for administration of inactivated vaccines.

          -  Concomitant use of the following medications

               1. Any investigational anticancer therapy.

               2. Any concurrent chemotherapy, immunotherapy, or biologic therapy. Concurrent use
                  of hormones for non-cancer-related conditions (e.g., insulin for diabetes and
                  hormone replacement therapy) is acceptable.

               3. Immunosuppressive medications including, but not limited to systemic
                  corticosteroids (>10 mg/day prednisone or equivalent), methotrexate,
                  azathioprine, and tumor necrosis factor alpha (TNF-α) blockers. Use of
                  immunosuppressive medications for the management of investigational
                  product-related AEs, in subjects with contrast allergies is acceptable. In
                  addition, use of inhaled and intranasal corticosteroids is permitted.

          -  Known contraindications to radiotherapy