Propagation of two-dimensional transient waves in multilayered viscoelastic media is investigated. The multilayered medium consists of N different isotropic, homogeneous and linearly viscoelastic layers with more than one discrete relaxation time. The top surface of the layered medium is subjected to dynamic in-plane surface tractions; whereas, the lower surface is free or fixed. A numerical technique which combines the Fourier transform with the method of characteristics is employed to obtain the solutions. The numerical results are displayed in curves denoting the variations of the stress and displacement components with time at different locations. These curves reveal clearly the scattering effects caused by the reflections and refractions of waves at the boundaries and at the interfaces of the layers. The curves also display the effects of viscous damping in the wave profiles. By suitably adjusting the material constants, curves for the cases of elastic layers and viscoelastic layers with one relaxation time (standard linear solid) are also obtained. The curves further show that the numerical technique applied in this study is capable of predicting the sharp variations in the field variables in the neighborhood of the wave Fronts. Solutions for some special cases, including Lamb's problem for the elastic half-space, are obtained and compared with the existing solutions in the literature; very good agreement is found. (C) 2001 Academic Press.