In the present work, the propagation of weakly non-linear waves in a prestressed thin viscoelastic tube filled with an incompressible inviscid fluid is studied. Considering that arteries are initially subjected to a large static transmural pressure P-0 and an axial stretch ratio lambda(z), and in the course of blood flow, a finite time-dependent displacement is added on this initial field, the governing non-linear equation of motion in the radial direction is obtained. Using the reductive perturbation technique, the propagation of weakly non-linear waves in the long wave approximation is examined. The general equation is obtained in the long-wave approximation, and it is shown that by a proper scaling, this equation reduces to the well-known non-linear evolution equations. Intensifying the effect of non-linearity in the perturbation process, the modified forms of these evolution equations are also obtained. (C) 1997 Elsevier Science Ltd.