Sorfenib works by slowing the spread of cancer cells. It has been used in other studies for patients with AML with the FLT3-ITD mutation and information from these studies suggests that sorafenib may help to control leukemia. The purpose of this study is to find the highest dose of sorafenib for maintenance therapy that can be safely used in participants with AML who have undergone allogeneic stem cell transplant.

Subjects will taken sorafenib orally either once or twice daily. Subjects will come to the Bone Marrow Transplant Clinic 3 times (on Day 8, 15, and 30) during the first month of treatment. After the first month, they will be seen every month for 3 months and then at 9 at 6 and 9 months. Subjects will have a physical exam and be asked questions regarding general health and specific questions about any problems they might be having and any medications they are taking.

Subjects will have standard blood tests every month for 12 months to check liver and kidney function and complete blood count.

Subjects will have research blood tests on Days 8, 15 and 30 during the first month of treatment.

Subjects will have a bone marrow biopsy after 3 months and 12 months of treatment.

Subjects will receive treatment for up to 12 months and be followed for 1 year after completing the study.

Inclusion Criteria:

• Subjects with AML with the FLT3-ITD mutation who have undergone allogeneic HSCT
• Peripheral blood chimerism studies showing >/= 70% of all cells are of donor origin
• Adequate hematologic and hepatic function
• ECOG performance status 0-2
• Able to swallow whole pills

Exclusion Criteria:

• Evidence of relapsed/recurrent/residual disease as assessed by bone marrow aspirate and biopsy performed between days 30-60 after HSCT
• Active acute graft vs host disease requiring an equivalent dose of > 0.5 mg/kg/day of prednisone or equivalent or those patients which necessitated the addition of another agent for the treatment of GVHD beyond corticosteroids
• Ongoing uncontrolled infection
• Cardiac disease: congestive heart failure > class II NYHA, unstable angina or new onset angina (began within the last 3 months) or myocardial infarction within the past 6 months
• Cardiac ventricular arrhythmias requiring anti-arrhythmic therapy
• Uncontrolled hypertension
• Known HIV infection or chronic hepatitis B or C
• Thrombotic or embolic events such as cerebrovascular accident including transient ischemic attacks within the past 6 months
• Pulmonary hemorrhage/bleeding event > CTCAE v 4.0 Grade 2 within 4 weeks of starting study drug
• Any other hemorrhage/bleeding event > CTCAE v. 4.0 Grade 3 within 4 weeks of starting study drug
• Serious non-healing wound, non-healing ulcer, or bone fracture
• Evidence or history of bleeding diathesis or coagulopathy
• Major surgery or significant traumatic injury within 4 weeks of starting study drug
• Use of St. John's Wort or rifampin (rifampicin)
• Known or suspected allergy to sorafenib
• Pregnant or breast-feeding
• Receiving any other investigational agents