A longitudinally compliant PTFE graft is provided by compressing at least a portion of a porous PTFE tube along its longitudinal axis and coating at least the outer wall of the compressed portion of the PTFE tube with a biocompatible elastomer for allowing the compressed portion of the tube to be stretched along the longitudinal axis. The PTFE tube is compressed by pulling the tube over a cylindrical mandrel of like diameter and applying a compression force to the tube along its longitudinal axis. The compressed portion(s) is (are) secured against movement upon the mandrel, and a coating of liquified polyurethane or other biocompatible elastomer is then applied over at least the compressed portion(s) of the tube. The elastomeric coating may be applied by dip coating or spray coating techniques. After the elastomeric coating has dried, the completed graft is removed from the mandrel.