This paper deals with the numerical modelling of seismic waves propagation in soils. Some essential aspects of numerical dispersion are firstly discussed. Classical numerical approaches for the modelling of damping are compared with physical approaches. A rheological model corresponding to classical Rayleigh damping is considered. The link with wave propagation centrifuge experiments is then made. From these tests, homogeneous damping does not appear to be a suitable assumption to analyse the whole experimental results. Many other experimental results on sand (cyclic, resonant...) also give evidence to the dependence of damping on mean stress. This paper then presents a numerical modelling of non-homogeneous damping of seismic waves in sand. Numerical computations involving mean-stress dependent damping are performed to model spherical wave propagation in the centrifuged medium. We consider different laws giving attenuation versus mean stress (Hardin, Saxena, Stewart). Finite element computations, involving these various influences of mean stress on damping, are performed. Numerical investigations give some interesting results on wave propagation through non-homogeneously damped medium. It leads to a good numerical quantification of damping phenomena in the whole medium by taking into account the mean-stress dependence.