This paper is concerned with the analysis of pressure transients in damageable elasto-plastic piping systems. The fluid dynamics and pipewall deformation are modelled by the classical water hammer theory, whereas pipewall mechanical behavior is described by an internal variable constitutive theory. The constitutive model coupling plasticity and damage used herein gives rise to a nonlinear hyperbolic problem in which the wavespeeds are altered by damage evolution. The problem is numerically approximated by means of a technique based on an additive decomposition together with the Glimm's method and a special Euler-type time integration scheme. Examples concerning the structural integrity analysis of a reservoir-pipe-valve installation, where hydraulic transients are generated by valve slam, are presented to illustrate the applicability of both theory and numerical method.