The branching technique demonstrated an effective ability to attenuate severe hydraulic-head magnitudes into existing steel-pipes-based hydraulic systems. However, there was no detailed exploration of circumferential-stress, radial-strain, and wave-oscillation period behaviors, which are equally embedded in the design stage of hydraulic systems. Accordingly, this paper examined these last parameters to provide relevant information on the entire design key parameters. The numerical solver used the Method of Characteristics for discretizing the extended one-dimensional water-hammer model incorporating the Vitkovsky and the Kelvin–Voigt formulations along with the discrete gas cavity model to represent column separation. The plastic short-penstock material types utilized in this study included high- or low-density polyethylene (HDPE or LDPE). Results demonstrated that the branching technique is promising in terms of hydraulic-head attenuation waves; however, this research emphasized the limitation of this technique, not previously delineated, including the amplification of the radial-strain peaks or crests and the spreading of the wave-oscillation period. Ultimately, a methodology was suggested for optimizing the plastic short-penstock diameter and length parameters.