Aim To study the boundary element method of the dynamical response of viscoelastic thin plates. Methods In the first place

the mathematical model of the dynamical response of viscoelastic thin plates is established in physical space

then the fundamental equation in Laplace domain is obtained by using Laplace transformation. Using both the fundamental solution of the fundamental equation and the boundary element method

the boundary integral equation in Laplace domain are obtained and solved numerically. The results of the original program are given by taking the numerical transform inversion. Results The deflection time curves and the bending moment time curves of the circular plate and the annular plate are given. Conclusion According to these figures the varying relation of deflection and time

also bending moment and time

is obtained.