Biot theory [l] is a basic tool when studying the propagation of elastic waves in porous/fibrous solids. Due to the simplicity of the assumptions, isotropic materials are most often utilized [2,3]. However, in some cases, anisotropy has to be included in the modelization, e.g. with some fibrous materials. In this work, we have developped routines, based on the standard Biot model, which compute the various characteristic surfaces (slowness, phase and group velocities) [4] in a given plane for anisotropic porous media. By increasing the weight of the coupling constants, one can continuously vary from the limit case of anisotropic solids with no porosity to a number of different porous media. When the coupling terms are not equal to zero, one finds four instead of three propagating modes, the two other eigenvalues being complex, meaning in turns that the two remaining solutions do correspond to some evanescent modes. The slow transverse mode is unchanged. The fourth mode often called the Biot mode [5], which is very similar to the pseudo-thermal wave [6,7] observed in dynamic thermoelasticity, has always a very small wavespeed and is very highly damped.