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In this paper, the possibility of reducing pressure surges in a quasi-rigid pipe network by replacing one of the pipes of the network by a viscoelastic one is examined. The mathematical model consists of a system of two hyperbolic, partial differential equations which are resolved by the method of characteristics using linear interpolation. The calculation at the network junctions is realised by resolving a linear system of equations including the manner various boundary conditions are introduced into the solution. The behaviour law of the viscoelastic pipe is described by the Kelvin-Voigt model. In order to simplify calculations, only the elastic element of this model is considered. For the applications, a constructed computer progrmn written in FORTRAN language is elaborated. The numerical results show the effect of the pipe wall elasticity on the damping of the pressure waves in the networks. [ABSTRACT FROM AUTHOR]