Abstarct: Mathematical modeling of piping systems, in which the dynamic behavior of the pipe system are also studied due to water hammer phenomenon, has been studied in recent years. Also consider the many benefits of viscoelastic pipes, these pipes are used in numerous industrial sectors, especially in piping systems is growing rapidly. In viscoelastic materials, the effect of loading on them, an additional deformation ( late ), the deformation is made, immediately after this occurs. The mathematical model presented earlier in viscoelastic study of water hammer in pipes, the Poisson ratio was assumed constan. While the modified mathematical mode, the Poisson ratio of the pipe varies with time is considered. In this study, first, partial differential equations governing water hammer in pipe systems made of viscoelastic materials is introduced. These equations are derived assuming a Poisson's ratio of pipe varies with time, constant bulk modulus of pipe and thin -walled pipe are done. From the physical point of view, the problem of water hammer, viscoelastic behavior leads to strain in the radial direction of the pipe axis is delayed. Should be noted that the axial strain due to inhibition of delayed pipe in the axial direction is considered to be zero. The differential equations are derived to calculate the strain delay, the convolution integral is used phrases which are calculated using an approximate relationship for good. After specifying the differential equations and initial and boundary conditions, a numerical method of characteristic (MOC) in order to solve the equations in the time domain to be handled. The results for a certain point of time-pressure in the history of the laboratory results are plotted with the pipe provided in the previous valid reaserches are compared. The results of this study suggest that by taking the Poisson ratio of the viscoalastic pipe varies in mathematical model, provided the answer cause high-precision on the water hammer phenomenon in viscoalastic materials for different discharge using a calibrated creep curves.