Inclusion Criteria:

- Diagnosis of 1 of the following: Acute myeloid leukemia (Acute promyelocytic leukemia
(M3) allowed provided patient has failed prior therapy with both tretinoin and
arsenic alone or in combination); Acute lymphoblastic leukemia; Myelodysplastic
syndromes; Blastic phase chronic myelogenous leukemia (Failed OR intolerant to
imatinib mesylate)

- Must have failed prior therapy with >= 1 cytotoxic- or biologic-targeted agent (e.g.,
hypomethylating agents, farnesyl transferase inhibitors, thalidomide, or tyrosine
kinase inhibitors); Any number of prior regimens allowed

- Performance status: ECOG 0-1

- ALT =< 2.5 times upper limit of normal

- Bilirubin =< 1.5 mg/dL

- Creatinine =< 2.0 mg/dL OR Creatinine clearance >= 60 mL/min

- Fertile patients must use effective contraception

- No psychiatric illness or social situation that would preclude study compliance

- Prior bone marrow transplantation allowed

- At least 2 weeks since prior cytotoxic agents OR at least 5 half-lives for
non-cytotoxic agents in the absence of rapidly progressing disease

- At least 24 hours since prior hydrea for control of peripheral blood leukemia cell
counts

- Hydroxyurea allowed up to 72 hours after start of therapy with sorafenib

- No persistent, chronic, clinically significant toxicities > grade 1 from prior
chemotherapy

Exclusion Criteria:

- Cytopenias secondary to multilineage bone marrow failure allowed

- Ineligible for or not willing to undergo allogeneic stem cell transplantation OR no
donor available

- Absolute blast count=< 20,000/mm^3 unless patient has documented fms-like tyrosine
kinase 3 internal tandem duplication

- No evidence of bleeding diathesis (except due to low platelets associated with the
primary disease)

- No New York Heart Association class III or IV congestive heart failure

- No uncontrolled hypertension (i.e., sustained systolic blood pressure [BP] >= 150 mm
Hg or diastolic BP >= 90 mm Hg)

- No unstable angina pectoris

- No symptomatic cardiac arrhythmia requiring and not responding to medical
intervention

- Not pregnant or nursing

- No history of allergic reaction attributed to compounds of similar chemical or
biological composition to the study drug

- No swallowing dysfunction that would impede oral ingestion of tablets

- No active uncontrolled infection

- No other uncontrolled illness

- No prior sorafenib

- No other concurrent investigational or commercial agents, except for standard
intrathecal chemotherapy for the treatment of isolated CNS leukemic involvement

- No other concurrent anticancer agents

- No concurrent combination antiretroviral therapy for HIV-positive patients

- No concurrent therapeutic anticoagulation (Concurrent prophylactic anticoagulation
[i.e., low-dose warfarin, catheter flushing with heparin] of venous or arterial
access devices allowed)

- No concurrent cytochrome P450 enzyme-inducing antiepileptic agents, including, but
not limited to, any of the following: Phenytoin; Carbamazepine; Phenobarbital;
Rifampin

- No concurrent Hypericum perforatum (St. John's wort)