Plastic material pipes such as high- or low-density polyethylene (HDPE or LDPE) are increasingly used in new or renewed water supply systems. Therefore, analysis of water hammer surge-waves initiated into such piping systems deserves investigation. The 1-D pressurized-pipe flow model embedding the Ramos formulation was used to describe the flow behavior in the elastic and plastic pipe-based hydraulic system. Numerical computations were performed using the method of characteristics. First, the numerical solver was validated against experimental data, available from the literature. Then, the proposed solver was applied to explore the transient pressure-wave behavior resulting from the power failure to a pumping station. Results evidenced the severity of such a scenario with regards to induced positive and negative pressure-wave magnitudes. Furthermore, the findings of this study suggested that plastic pipe-wall materials allowed a significant attenuation of pressure-wave magnitude in conjunction with the expansion of the pressure-wave oscillation period. It was also found that the observed attenuation and expansion effects depended strongly upon the plastic material type. In this respect, the results revealed that LDPE provided a better trade-off between the two last effects than HDPE.