Cavitation damaging is investigated by simulation of the model problem of a single gas bubble in a compressible liquid collapsing near the surface of an elastic solid wall. The three-phase system is described by the compressible Euler equations supplemented by the stiffened gas law for both fluids, a non-conservative evolution equation for the gas fraction characterizing the liquid-gas interface and the elastodynamical equations for a linear-elastic solid. The fluid model and the solid model are coupled by transition conditions at the fluid-structure interface. The fluid equations are discretized according to Saurel and Abgrall and for the elastodynamical equations a finite volume discretization is applied. These numerical methods are coupled by a weak coupling strategy. The numerical results exhibit von Schmidt waves in the structure as well as the fluid. As possible explanation for cavitation damaging the von Mises yield criterion is evaluated.