Abstract: Based on von Karman thin plate theory and Boltzmann principle for linear viscoelastic materials, the nonlinear integral-partial differential dynamic equations for viscoelastic symmetrically laminated plates are derived. By using the Galerkin procedure, Newmark scheme and Newton-Cotes method, an effective numerical method is developed to perform the nonlinear dynamic analysis of viscoelastic laminated structures with hereditary constitutive relationship and relax modulus expressed in Prony series. Some numerical examples are given and the results are compared with available data.