Abstarct: Due to the great benefits of viscoelastic pipes, the use of such pipes in various systems is increasing rapidly. The viscoelastic behavior of polymer pipes must be considered for water hammer signal analysis. The water hammer phenomenon is the increase in pressure that occurs in fluids after a change of direction or a sudden closure of the flow path, and this increase in pressure often occurs when a valve closes in the path of the fluid. The Kelvin–Voigt method is used to model the viscoelastic behavior of the pipe. In this model, the spring, along with a number of different elements of the spring and dashpot in a parallel composition, are in series. Viscoelastic pipes show a continuous time-dependent behavior on the applied stresses. Retarded strain term in relation to continuity depends on time, pressure and creep coefficients. In linear viscoelasticity, the relationship between strain and pressure is linear and the creep coefficients are defined as constant numbers. In the discussion of nonlinear viscoelasticity which is the main subject of this research, creep compliance coefficients are defined in terms of pressure. In the first part of this study, the effect of the number of Kelvin-Voigt elements on the creep function of viscoelastic pipes and pressure fluctuations due to water hammer is investigated. In this part, the creep coefficients of one to four-element Kelvin-Voigt models are determined using the creep function obtained from the five-element Kelvin-Voigt model, which is given by Covas et al. for discharge 1 L/s, and pressure fluctuations of water hammer at the end of pipes with lengths of 20 to 8000 meters. The results of this part show that the accuracy of three and four element models in pipes with a length of more than 1000 meters in the first method is higher than the second method and for lengths less than 1000 meters the accuracy of three and four element models in both methods is the same. In the two-element model, for pipes longer than 720 meters, the accuracy of the first method is higher than the second method and for lengths less than 720 meters, the results are the opposite. Error analysis of both methods shows that the model of one element is largely incorrect and therefore not suitable for predicting transient pressures in viscoelastic pipes. In the second part of this study, first the effect of linear viscoelasticity and unsteady friction on the results of pressure due to water hammer is investigated and then the nonlinear behavior of the viscoelastic pipe in the water hammer phenomenon is investigated. Investigation of the effect of unsteady friction and linear viscoelasticity on pressure results has shown that unsteady friction has little effect on the results and its effect in the study of nonlinear behavior of viscoelastic pipe is neglected. To investigate the nonlinear behavior of viscoelastic pipes, high loading rates (pressures obtained from the Joukowski relation) and creep coefficients of the Kelvin-Voigt model were determined using the water hammer model for different flow rates and for each creep compliance coefficient a relation in terms of pressure has been extracted. In the next step, these relations are applied in the water hammer numerical model and it is possible to calculate the creep compliance coefficients for different flows and use them to predict pressure fluctuations and compare with the results of the linear viscoelastic model. In this research, linear interpolation method has been used to determine the creep coefficients of some flows and then pressure fluctuations have been predicted using the water hammer numerical model. Comparison of the results of interpolation method and nonlinear model with laboratory values and linear model shows that the proposed relationships and creep coefficients obtained from the interpolation method predict the pressure fluctuations well and the nonlinear model has better accuracy than the linear model due to the use of different creep functions. In this study, using the obtained creep coefficients, the creep function of different flow rates has been determined and the results have shown that with increasing pressure, the amount of creep of the viscoelastic tube increases.