A body compatible stent is formed of multiple filaments arranged in at least two sets of oppositely directed helical windings interwoven with one another in a braided configuration. Each of the filaments is a composite including a central core and a case surrounding the core. In the more preferred version, the core is formed of a radiopaque and relatively ductile material, e.g. tantalum or platinum. The outer case is formed of a relatively resilient material, e.g. a cobalt/chromium based alloy. Favorable mechanical characteristics of the stent are determined by the case, while the core enables in vivo imaging of the stent. The composite filaments are formed by a drawn filled tubing process in which the core is inserted into a tubular case of a diameter substantially more than the intended final filament diameter. The composite filament is cold-worked in several steps to reduce its diameter, and annealed between successive cold working steps. After the final cold working step, the composite filament is formed into the desired shape and age hardened. Alternative composite filaments employ an intermediate barrier layer between the case and core, a biocompatible cover layer surrounding the case, and a radiopaque case surrounding a structural core.