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The stability of axially accelerating viscoelastic beams is a significant problem that has been studied analyvtically and numerically[1-3].However.those investigations focused on Euler-Bernoulli beams.The numerical investigation on Timoshenko beams has never been reported before, although some analytical results have been achieved[4,5].In this paper, based on the governing equation[5].the simulation of axially accelerating viscoelastic beam undergoing parametric resonance is performed to locate the stability regions.The axial speed of the beam is characterized as a simple harmonic variation about the constant mean speed.The finite difference schemes are developed to solve the governing equations numerically.The stability regions of parametric resonances are numerically determined.