This research study involves the use of two investigational drugs: sorafenib and bortezomib. Sorafenib is designed to stop the growth of cells caused by changes associated with cancer. Bortezomib is designed to stop cancer cells from getting rid of waste products. This causes the cells to build up toxic levels of waste that leads to cell death. In the laboratory, the combination of sorafenib and bortezomib has been shown to fight cancer cells better than either drug alone. We are looking to determine if the combination of sorafenib and bortezomib is a safe treatment for patients with advanced melanoma. The effectiveness of this combination will also be assessed.

• Since we are looking for the highest dose of the study drug that can be administered safely without severe or unmanageable side effects in participants that have melanoma, not everyone who participates will receive the same dose of the study drug. The dose participants will get will depend upon the number of participants who have been enrolled in the study before and how well they tolerated their doses.
• Each treatment cycle lasts 28 days. Participants will take sorafenib orally twice a day and will receive bortezomib as an out-patient intravenous injection on Days 1, 8 and 15 of every cycle.
• At the end of each treatment cycle, participants will be examined to determine whether their disease has worsened, improved or stayed the same, and to see if they are experiencing any side effects of treatment. The following tests will be done at these visits: physical examination, vital signs, blood tests and scans (repeated every 2 months).
• Once the maximum tolerated dose of sorafenib and bortezomib have been determined, an additional 12 participants will be enrolled in this study. This is called the expansion cohort of this study. Participants enrolled in this cohort will be required to undergo a biopsy of the tumor lesion before they start study treatment and an additional biopsy after you start study treatment.

Inclusion Criteria:

• Histological or cytological confirmation of malignant melanoma that is metastatic or unresectable
• Measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension as 10mm or greater with spiral CT scan
• Patients may have received up to 4 prior treatments for their disease including immunotherapies such as high-dose interleukin 2 and antibodies directed against the human cytotoxic T-lymphocyte antigen 4
• 18 years of age or older
• Life expectancy of greater than three months
• ECOG Performance status of 0 or 1
• Adequate organ and marrow function as outlined in the protocol
• Women of childbearing potential must have a negative serum pregnancy test performed within 7 days prior to the start of treatment
• INT < 1.5 or a PT/PTT within normal limits. Patients receiving anti-coagulation treatment wih an agent such as warfarin or heparin may be allowed to participate. For patients on warfarin, the INR should be measured prior to initiation of sorafenib and monitored at least weekly, or as defined by the local standard of care, until INR is stable
• Women of child-bearing potential and men must agree to use adequate contraception prior to study entry and for the duration of study participation.

Exclusion Criteria:

• Chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events dur to agents administered more than 4 weeks earlier
• Participants may not be receiving any other study agents
• Known, active CNS disease, including primary brain tumor, seizures not controlled with standard medical therapy, any unstable or untreated brain metastasis, or history of stroke within the past 12 months
• Prior therapy with bortezomib, sorafenib, or other proteasome inhibitor
• History of allergic reactions attributed to compounds of similar chemical or biologic composition to sorafenib and bortezomib
• Participants receiving any medications or substances that are inducers of CYP3A4
• Known cardiac disease including congestive heart failure > class II NHYA, unstable angina or new onset angina, myocardial infarction within the past 6 months, or electrocardiographic evidence of acute ischemic or active conduction system abnormalities. Prior to study entry, any ECG abnormality at screening has to be documented by the investigator as not medically relevant
• Cardiac ventricular arrhythmias requiring anti-arrhythmic therapy
• Uncontrolled intercurrent illness
• Pregnant women
• Individuals with a history of a different malignancy are ineligible except for the circumstances outlined in the protocol
• HIV-positive individuals on combination antiretroviral therapy
• Uncontrolled hypertension despite optimal medical management
• Thrombolic or embolic events
• Pulmonary hemorrhage/bleeding event CTCAE Grade 2 or greater within 4 weeks of first dose of study drug
• Any other hemorrhage/bleeding event CTCAE Grade 3 or greater within 4 weeks of first dose of study drug
• Serious non-healing wound, ulcer or bone fracture
• Evidence or history of bleeding diathesis or coagulopathy
• Major surgery, open biopsy or significant traumatic injury within 4 weeks of first study drug
• Any condition that impairs patient's ability to swallow whole pills
• Any malabsorption problem
• Known hypersensitivity to boron or mannitol
• Grade 2 or greater peripheral neuropathy within 14 days before enrollment