Abstract: A numerical method is presented for simulating wave propagation in a viscoelastic media with an irregular boundary. The standard linear solid (SLS) mechanism is used to characterize the viscoelastic media. The stress formulae for recursive calculation are derived from SLS constitutive relations. The dynamic equilibrium equations of controlled volumes are established by using the mesh of triangular grid. By applying the dynamic equilibrium equations of controlled volumes and the stress formulae alternately, the nodal accelerations, velocities, displacements, and the stresses in each grid can be obtained in time domain. The result comparing with the analytical solution shows that the numerical algorithm presented is an effective method. The free boundary condition of arbitrary irregularity is satisfied naturally. The dynamic concentration phenomena of shear stress and accelerations are investigated for the area of Beichuan county town with a topography surface. The seismic disaster reasons of the Beichuan county town are analyzed.