This study analyzes the effect of the pipe material type on the transient flow behavior in a pumping system due to an accidental pump shutdown. The material types addressed in this study include steel and high- or low-density polyethylene (HDPE) or (LDPE), involving elastic and plastic rheological pipe-wall behavior. The numerical solution is developed based on the method of characteristics used for the discretization of the extended one-dimensional pressurized-pipe flow model, incorporating the Kelvin-Voigt and Vitkovsky rules. Experimental data from the literature were used to validate the numerical solver. The proposed numerical algorithm is then used to investigate the transient pressure-wave behavior induced by the power failure to a pumping station composed of an inline connection using different pipe material types. The findings show the severity of such a scenario, in terms of the magnitudes of induced up-surge and down-surge pressure waves. Furthermore, this research demonstrates that plastic pipe-wall materials allow for substantial attenuation of surge magnitude in conjunction with the expansion of the period of pressure-wave oscillations. The observed attenuation and expansion effects are also found to be highly dependent on the plastic material type. In this respect, the findings indicate that the (LDPE-steel) piping system's specific layout allows for the best tradeoff between the two last effects.