We integrate the magnetohydrodynamics (MHD) ideal equations to simulate dark void sunwardly moving structures in post-flare supra-arcades. We study the onset and evolution of the internal plasma instability to compare with observations and to gain insight into physical processes and characteristic parameters of these phenomena. The numerical approach uses a finite-volume Harten–Yee total variation diminishing (TVD) scheme to integrate the 1D 1/2 MHD equations specially designed to capture supersonic flow discontinuities. The integration is performed in both directions, the sunward radial one and the transverse to the magnetic field. For the first time, we numerically reproduce observational dark voids described in Verwichte et al. We show that the dark tracks are plasma vacuums generated by the bouncing and interfering of shocks and expansion waves, upstream an initial slow magnetoacoustic shock produced by a localized deposition of energy modelled with a pressure perturbation. The same pressure perturbation produces a transverse to the field or perpendicular magnetic shock giving rise to non-linear waves that compose the kink-like plasma void structures, with the same functional sunward decreasing phase speed and constancy with height of the period, as those determined by the observations.