It is well known in the literature that standard hierarchical matrix (H-matrix) based methods, although very efficient for asymptotically smooth kernels, are not optimal for oscillatory kernels. In a previous paper, we have shown that the method should nevertheless be used in the mechanical engineering community due to its still important data-compression rate and its straightforward implementation compared to H 2-matrix, or directional, approaches. Since in practice, not all materials are purely elastic it is important to be able to consider visco-elastic cases. In this context, we study the effect of the introduction of a complex wavenumber on the accuracy and efficiency of H-matrix based fast methods for solving dense linear systems arising from the discretization of the elastodynamic (and Helmholtz) Green's tensors. Interestingly, such configurations are also encountered in the context of the solution of transient purely elastic problems with the convolution quadrature method. Relying on the theory proposed in [12] for H 2-matrices for Helmholtz problems, we study the influence of the introduction of damping on the data compression rate of standard H-matrices. We propose an improvement of H-matrix based fast methods for this kind of configuration. This work is complementary to the recent work [12]. Here, in addition to addressing another physical problem, we consider standard H-matrices, derive a simple criterion to introduce additional compression and we perform extensive numerical experiments.