The attenuation of small perturbations in the shape of a plane shock wave is studied for three distinct cases — (A): when a rigid boundary (wall) parallel to the plane of the unperturbed shock is present; (B): when a perturbed interface between two different media exists in the wake of the shock; (C): when there is no boundary (free space). The solution is obtained by extension of a method due to Zaidel. It is shown that for weak shock waves the attenuation becomes very weakly dependent on the nature of the boundary. Numerical results are obtained for shock waves with initially sinusoidal perturbations and initially Gaussian perturbations. For initially sinusoidal perturbations, Case (A) shows the slowest damping (highest peak‐to‐peak ampli‐after some time) whereas Case (B) exhibits the most rapid damping. On the other hand, an initially Gaussian perturbation shows the slowest damping (magnitude of maximum disturbance) for Case (B) and the fastest damping for Case (A). Furthermore, the Gaussian perturbation damps monatonically with time whereas the sinusoidal perturbation damps approximately in the manner of a zero‐order Bessel function — i.e., in an oscillating fashion.