This is an open-label Phase I dose-escalation safety study of VELCADE in combination with pralatrexate in patients with previously treated multiple myeloma. In a standard 3+3 dose escalation trial design, escalating doses of pralatrexate in combination with VELCADE will be studied sequentially, with at least 3 patients in each dose level until the MTD is determined. Dose limiting toxicity (DLT) and MTD are determined during cycle 1 of treatment.