The flow arising from an initial pressure discontinuity across a perturbed interface of two ideal gases is studied using analytical and numerical methods. In particular, the stability of the shock wave, the interface, and the rarefaction wave in the resulting flow are investigated. The equations of motion and the initial and boundary conditions are linearized for small perturbations, and a Fourier analysis is made in the lateral direction. The equations are then solved by the method of characteristics. The results show that the interface is unstable and its perturbations asymptotically acquire a constant rate of growth. The shock wave is stable and has rapidly damped oscillations, which appear to be unaffected by the instability of the interface.