The paper focuses on the numerical treatment of transient acoustic problems using finite element (FE) and boundary element (BE) methods. The FE method relies on a pressure formulation and the use of an implicit integration schemes for solving the related second-order differential system. The procedure is shown on cavity (interior) problems but can be extended to exterior problems using the DtN (Dirichlet-to-Neumann) approach. The presented BE method is restricted to 3-D problems and is based on the Kirchhoffs integral representation. The related retarded potential technique presents some interesting features which are stressed: the sparseness of matrices, the particular integration tools required and the time integration procedure for getting boundary variables. An enhanced procedure for reducing the memory requirements is also presented. Numerical applications show the performances of these discrete techniques.