The response of coated, metallic structures subjected to shock pressure waves is studied. The coating is either an elastic material or nearly incompressible rubber of variable stiffness separating the structure from an air or water medium. The stress, nodal velocity, and internal energy of the coated structure are compared to a system without a coating (homogeneous system) to examine the effect of various coating types and configurations on the response of the structure to shock conditions. The results show that a mismatch of impedance, pc0, between the coating and structure governs the degree of energy exchange between the coating and structure at the interface. The impedance mismatch between the structure and a rubber coating at the threshold value is termed the critical difference. If the impedance mismatch exceeds the critical difference, the dynamic response will be more adverse. A softer coating generally has a smaller impedance and tends to concentrate stress wave energy in the underlying structure.