The Richtmyer–Meshkov instability of interfaces separating elastic-plastic materials from vacuum is investigated by numerical simulation using a multi-material solid mechanics algorithm based on an Eulerian framework. The research efforts are directed to reveal the influence of the initial perturbation and material strength on the deformation of the perturbed interface impacted by an initial shock. By varying the initial amplitude $(kξ_0)$ of the perturbed interface and the yield stress $(σ_{\Upsilon}),$ three typical modes of interface deformation have been identified as the broken mode, the stable mode and the oscillating mode. For the broken mode, the interface width (i.e., the bubble position with respect to that of the spike) increases continuously resulting in a final separation of the spike from the perturbed interface. For the stable mode, the interface width grows to saturation and then maintains a nearly constant value in the long term. For the oscillating mode, the wavy-like interface moving forward obtains an aperiodic oscillation of small amplitude, namely, the interface width varies in time slightly around zero. The intriguing difference of the typical modes is interpreted qualitatively by comparing the early-stage wave motion and the commensurate pressure and effective stress. Further, the subsequent interface deformation is illustrated quantitatively via the time series of the interface positions and velocities of these three typical modes.