Shock-wave interaction with an elastic structure is investigated using a coupled numerical analysis approach, which considers solid-fluid interaction within an arbitrary Lagrangian-Eulerian framework. The analysis is performed considering a compressive shock wave, where the shock front is followed by constant pressure. An analysis procedure, which considers the change in the fluid domain due to the deformation of the solid and changes in the overpressure due to the movement of the elastic structure, is developed. Approximate numerical procedures for solving the Riemann problem associated with the shock are implemented within the Godunov finite volume scheme for the fluid domain. The influences of parameters such as structural stiffness and mass of the system on the displacement, velocity, and energy of the elastic structure following the shock-wave incidence are investigated. Immediately after the contact of the shock wave with the solid surface the pressure at the face of the elastic solid rises to a value which is equal to that obtained off of a fixed rigid wall. Subsequently, the motion of the piston produces changes in the applied pressure. The overpressure applied to the elastic system does not have a fixed profile but it depends on its elastic stiffness and structure mass. It is shown that there is a continuous exchange of energy between the air and the moving elastic structure, which produces a damped motion of the solid. The effect of damping is considerable for the cases of low elastic stiffness and low structural mass, where the resulting motion of the solid is nonoscillatory. The conventional analysis procedure, which ignores the energy exchange between the air and the moving solid, predicts an undamped oscillatory response of the structure for all cases considered. It is shown that neglecting the interaction between the air and solid can produce significant error in the total energy of the structure and the dynamic load factor when the resulting motion is nonoscillatory. © 2010 ASCE.