<p>In this paper, we consider numerical solutions of a two-dimensional time-dependent acoustic-elastic wave interaction problem imposed between a bounded penetrable elastic body and a compressible inviscid fluid. It is also called the fluid-solid interaction (FSI) problem. We first design an interior penalty discontinuous Galerkin (DG) method for the discretization of the interaction problem in space. The well-posedness on the semidiscrete discontinuous Galerkin equation is established, followed by an optimal priori error estimate in the energy norm. In principle, the transmission boundary conditions and the radiation boundary condition in the corresponding DG equation of the formulation employed in the current work make the Lax–Milgram theory not applicable, and it causes the main difficulty in the well-posedness and error analysis. We make a decomposition of the bilinear form into symmetrical and asymmetrical parts which will be considered separately, and utilize a basic theory of ordinary differential equations to accomplish the theoretical analysis. Numerical results are presented to confirm the accuracy of the proposed method.</p>