Wave propagation phenomena occur in all fields of science and engineering. Although there are several numerical methods available for the simulation of these phenomena it turns out that particularly, the Boundary Element Method is well suited for such problems. This volume addresses wave propagation through linear elastic continua – an interesting problem for civil, mechanical and geotechnical engineers. A main aim of this work is the development of an efficient and fast Boundary Element formulation with a time discretization based on the Convolution Quadrature Method.A crucial task within this scheme is the computation of the convolution weights which are commonly evaluated via approximations of Cauchy’s integral formula. Contrary to that, in this work closed-form expressions are developed. These expressions return nonzero values solely in a certain range of the argument – the basis for the construction of the efficiency improved formulation. Within this scheme hierarchical matrices are utilized to reduce the densely populated matrices to sparse ones.Numerical examples cover convergence studies as well as efficiency measurements in terms of computational effort and storage requirements. In view of the obtained results it turns out that the formulation is capable to significantly reduce the memory consumption as well as the computational effort. Besides some academic problems, an additional semi-infinite half space blasting physics problem is investigated as well.