A blood and body-tissue compatible synthetic polymer having mechanical compliance properties matching that of body tissue, useful in prosthesis as vascular grafts, skin covering, small diameter body duct work, and similar tissue replacement materials. A block copolymer having suitable body and blood compatibility characteristics is dissolved in a solvent, yielding a solution having an approximate relative viscosity between the range of 100 to 1000. A clean mandrel is slowly dipped into the solution and slowly withdrawn, leaving a uniform coating of polymer solution over the forming surface of the mandrel. The coated mandrel is then immersed into a second, nonsolvent solution which is miscible with the first solvent. The resulting transfer of the nonsolvent solution into the polymer network, displacing the first solvent molecules, acts to precipitate the polymer in a physical form containing a uniform dispersion of voids throughout the polymer structure. Such voids provide a mechanical response to the final polymer material which parallels that of natural arterial tissue, while at the same time retaining the necessary compatibility characteristics for prosthesis.