We present an efficient algorithm for rendering sweep surfaces using programmable graphics hardware. A sweep surface can be represented by a cross-section curve undergoing a spline motion. This representation has a simple matrix-vector multiplication structure that can easily be adapted to programmable graphics hardware. The data for the motion and cross-section curves are stored in texture memory. The vertex processor considers a pair of surface parameters as a vertex and evaluates its coordinates and normal vector with a single matrix multiplication. Using the GPU in this way is between 10 and 40 times as fast as CPU-based rendering.