DISEASE CHARACTERISTICS:

• 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
• Cytopenias secondary to multilineage bone marrow failure allowed
• Ineligible for or not willing to undergo allogeneic stem cell transplantation OR no donor available

PATIENT CHARACTERISTICS:

Age

• 18 and over

Performance status

• ECOG 0-1

Hematopoietic

• 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)

Hepatic

• ALT ≤ 2.5 times upper limit of normal
• Bilirubin ≤ 1.5 mg/dL

Renal

• Creatinine ≤ 2.0 mg/dL OR
• Creatinine clearance ≥ 60 mL/min

Cardiovascular

• 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

Other

• Not pregnant or nursing
• Fertile patients must use effective contraception
• 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 psychiatric illness or social situation that would preclude study compliance
• No other uncontrolled illness

PRIOR CONCURRENT THERAPY:

Biologic therapy

• See Disease Characteristics
• Prior bone marrow transplantation allowed

Endocrine therapy

• Not specified

Surgery

• Not specified

Other

• 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
• 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)