Abstract <p>During an earthquake, SH-waves propagate through the rocks within the Earth’s crust, causing the advancement of punches (localized stress concentrations) in the rock medium. This progression leads to significant stress accumulation around the propagating punch, which can impact the stability of geological and human-made structures, potentially leading to structural failure. Therefore, understanding the stress concentration near the moving punch driven by SH-wave propagation is crucial in seismological studies. This paper presents an analytical approach to examine the influence of the punch velocity associated with SH-wave propagation, on the dynamic stress concentration (DSC) in pre-stressed transversely isotropic double poroviscoelastic (TIDPV) rock media. A closed-form expression for DSC under a constant force intensity has been derived using the Wiener-Hopf technique, along with Galilean and two-sided Fourier integral transformations. The significant impact of various influencing parameters (viz. punch velocity associated with SH-wave propagation, horizontal and vertical initial compressive/tensile stresses, porosity, and anisotropy parameter) on DSC has been analyzed. Numerical computations and graphical illustrations for TIDPV rock media have been conducted to evaluate the profound impact of affecting parameters on DSC. Results indicate that increasing punch velocity amplifies DSC in double poro-viscoelastic media. Additionally, a comparative analysis of the influence of porosity on DSC across three viscoelastic rock media-transversely isotropic double poro-viscoelastic (TIDPV), transversely isotropic single poro-viscoelastic (TISPV), and isotropic double poro-viscoelastic (IDPV) – is graphically presented. The study highlights distinct characteristics of DSC in each medium, providing valuable insights into stress behavior under dynamic seismic conditions. Moreover, key insights and peculiarities have been identified from the derived DSC expression.</p>