Abstract: A mechanical model of anisotropic viscoelastic body is set up in this paper from the microstructure of the tooth of fibre reinforced plastic gears and the viscoelastic stress field is solved by the finite element method combined with the Laplace transformation technique.The Schaper's numerical inversion method is successfully improved by introducing a time converting factor and is used in this paper to transform the solution of the problem from the Laplace space to the physical space.It is found that the calculated results by the method presented are in good coincidence with tihe tested data.