Numerical simulations of the interaction of Mach 1.3 shock waves and gaseous interfaces between air and helium or SF6 were carried out using EAD, a 2D, second order non‐viscous Eulerian code. The interface, described either by a single sinusoidal wave or a combination of sinusoidal waves of random amplitudes is subjected to Rayleigh‐Taylor instability induced by the incident shock and successive waves reflected from the shock tube end wall. The evolution of the subsequent mixing zone thickness and the kinetic energy of the fluctuating velocity field associated with the mixing are extracted from the simulation and compared with theoretical estimates based on an quasi‐incompressible analysis of the instability.