In the present work, we studied the propagation of small bur finite amplitude waves in a prestressed thick-walled viscoelastic tube filled with ail incompressible inviscid fluid. In order to include the dispersion, the wall's inertial and shear effects are taken into account in determining the inner pressure-inner cross-sectional area relation. Using the reductive perturbation method, the propagation of weakly nonlinear waves in the long-wave approximation is investigated. After obtaining the general evolution equation in the long-wave approximation, by a proper scaling, it is shown that this general equation reduces to the well-known evolution equations such as the Burgers, Korteweg-deVries and Korteweg-deVries-Burgers equations. The variations of solution profile with initial deformation, thickness ratio and the viscosity coefficients an numerically evaluated and the results are illustrated in some figures. (C) 1998 Elsevier Science Ltd. All rights reserved.