Numerical computing software (via MathWorks MATLAB) has been developed to understand the relationship between shock wave passage in geological targets (i.e., heterogeneous media) and the formation of shock veins and associated high-pressure/ temperature polymorphs. This approach takes into consideration the pressure due to the passage of the shock front, subsequent rarefaction unloading pressures, and associated heating and cooling rates. The model is applied to calculate pressure-temperature-time conditions for coesite-and stishovite-bearing shock veins within metaquartzites of the Vredefort impact structure of South Africa. To constrain the model, the position of the host metaquartzites at the time of impact is first reconstructed. The developed code then passes the appropriate shock conditions through the target to re-create the shock wave, while simultaneously forming and cooling the shock veins via 2-D steady-state conduction. We have found that (1) at the time of shock vein formation (2.4 s following the initial contact of the projectile), the shock front pressure was 13.8 GPa and the width of the shock wave was of 27 km; (2) the melt within the shock veins initially reached ~3000 °C, which corresponds to the melting temperature of the target rock at 13.8 GPa. Simulation results indicate that conditions reach the stishovite stability field within 2 ms of vein formation (~10-14 GPa; 2000-3000 °C), followed by coesite within 1.29 s (~3-10 GPa; 600-2000 °C).The dwell time of the modeled shock vein system is 4.35 s. The shock vein system is completely solidified 33.4 s after the initial shock front passage. The calculated P-T-t path of the model indicates that the polymorphs within the shock veins of the metaquartzites at Vredefort formed under their normal stability field conditions following rarefaction wave decompression.