The purpose of this study is to test the safety of sorafenib and vorinostat when given together to see what effects (good and bad) it has on the patient and their acute myeloid leukemia (AML) or myelodysplastic syndrome (MDS). This study is also being done to find the highest dose of sorafenib and vorinostat that can be given together without causing severe side effects.

Inclusion Criteria:

• Patients must have a diagnosis of AML (> 20% myeloid blasts in the peripheral blood or bone marrow) or MDS with > 10% myeloid blasts in the bone marrow. Patients with Acute Promyelocytic Leukemia (APL) must be refractory to all-trans retinoic acid (ATRA) and arsenic trioxide.

• The patients must have one of the following criteria:

  • Age of 18 to 69 years; relapsed or refractory disease following at least one prior therapeutic regimen; not a candidate for cytotoxic or other conventional therapies due to disease refractoriness, poor performance status, or co-morbidities
  • Age of 70 years or older; received no previous therapies (other than hematopoietic growth factors or hydroxyurea); not a candidate for cytotoxic or other conventional therapies due to poor performance status, co-morbidities, or personal preference
  • Age of 70 years or older with relapsed or refractory disease

• The patient must have discontinued all previous therapies for acute leukemia for at least 14 days and recovered from the acute effects of the therapy.

• Patients must have an ECOG (Zubrod) performance status of 0-2

• Patients must be able to take and tolerate oral medications

• Patients must have adequate organ function as specified in the protocol.

• Patients not on anti-coagulation must have an INR < 1.5 and a PTT within normal limits.

Exclusion Criteria:

• Pregnant women or nursing mothers are not eligible for this trial.
• Patients may receive no other concurrent biologic therapy, cytotoxic chemotherapy or radiation therapy during this trial.
• Patients with one or more serious preexisting medical conditions that, in the opinion of the investigator, would preclude participation in this study. See protocol for listing.
• Patients with known central nervous system (CNS) leukemia by spinal fluid cytology, flow cytometry or imaging
• Patients with previous autologous or allogeneic stem cell transplantation who have current side effects and/or complications that in the opinion of the investigator can interfere with the interpretation of the toxicities.