Propagation of two-dimensional transient waves in viscoelastic cylindrical layered media is investigated. The cylindrical multilayered medium consists of N different isotropic, homogeneous and linearly viscoelastic layers with two discrete relaxation times. A numerical technique which combines the complex Fourier series 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, and the effects of viscous damping in the wave profiles. The curves further show that the numerical technique applied is capable of predicting the sharp variations in the field variables in the neighbourhood of the wave fronts. By suitably adjusting the material constants, the results for the special cases of elastic layers and viscoelastic layers with one relaxation time (standard linear solid) are also obtained. Furthermore, solutions for some special cases are compared with the available solutions in the literature and a good agreement is found. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.