The spline mandrel and barrel are formed with longitudinally extending, circumferentially spaced grooves in their outer and inner surfaces respectively. Composite splines are inserted into the grooves to key the mandrel and barrel together. Each spline comprises a rigid core having a slab of deformable material, such as urethane, bonded to the core face which slides and drives the driven tubular part. In a preferred form, the spline barrel is formed in two pieces. The spline-receiving grooves are formed at the upper end of the lower barrel section. The threaded pin of the upper barrel section locks the splines in the grooves. Because the splines are spaced downwardly from the end of the barrel, the mandrel has an ungrooved, thick-walled upper section which provides desired strength. Seals are provided at the upper end of the barrel and on the spline mandrel to form an annular chamber, containing the splines, filled with lubricant. The spline assembly is characterized by improved wear qualities relative to prior art assemblies.