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In this paper, a novel method based on nonuniform rational B-spline (NURBS) curves is proposed to simulate a physics-based muscle model for facial expression animation. In our system, nonuniform rational B-spline curves are used to construct facial muscles based on the anatomical knowledge. By changing the weights of the NURBS curves, we can form a motion vector to control facial muscle movements. With different number of control points, muscles are more controllable so that more detailed facial expression and mouth shapes can be simulated. Our approach can simulate different types of muscles including linear and sphincter muscles, as well as the nonlinear part of the face like fatty tissue.