We study a notion of capacity related to elasticity which proves convenient to analyze the concentrations of strain energy caused by the rigid displacements of some in nitesimal parts of an elastic body in two or three dimensions. By way of application, we investigate the behavior of solutions to initial boundary value problems describing vibrations of periodic elastic composites with rapidly varying elastic properties. More speci cally, we analyze a two-phase medium whereby a set of heavy sti tiny particles is embedded in a softer matrix. This task is set in the context of linearized elasticity.