Presently, a great part of the attention paid to the studies on the Richtmyer–Meshkov instability (RMI) is focused on the case of shock passage through a system of gas layers of different densities. The interest to this problem has been induced, in particular, by multiple attempts to minimize the process of mixing between the layers of different densities in targets for inertial confinement fusion (ICF), caused by excitation of the RMI on the layer boundaries. The RMI suppression is one of the most important, but difficult problems in worldwide efforts on ICF. A direct investigation of this phenomenon in laser experiments (in NOVA, for example) is a rather difficult task. Shock tubes are a more promising tool for modeling the impulsively-driven instabilities in gas layers, for they allow us a detailed investigation of the mechanism of initiation and the pathways of evolution of the instability (Jacobs et al. 1995; Aleshin et al. 1995a). A series of shock-tube experiments for the shock passage through a system of gas layers of different densities has been carried out. The effect of a suppression of the RMI has been found. A 2.5-fold reduction of the mixing region thickness in the presence of the layer as compared to the thickness without it has been obtained.