The instability of an interface between two media after the passage of twoshocks that follow one after the other at a certain time interval isstudied numerically. A simple formula suggested earlier (Charakhch'yan 2000 Prikl. Mekh. Tekh. Fiz.41 28-37) for reshocking afree aluminum surface is confirmed for shocks from aluminum to deuteriumice, from air to helium and from freon to air. The formula describesreshocking at the non-linear stage of the instability evolution and isindependent both of the wavelength of the initial perturbation and ofthe perturbation amplitude at the moment of reshocking. Both asinusoidal initial perturbation and a perturbation in the form of abroken line are considered. It is demonstrated that the parameters ofthe second shock that ensure the freeze-out phenomenon are determinedusing only the amplitude growth rate before reshocking.