Passive safety, particularly in the transport industry, requires maximizing the dissipation of energy and minimizing the decelerations undergone by a vehicle following a violent impact (crash). This paper proposes a strategy for identifying an anisotropic local damage criterion in a moderate dynamic loading for Advanced Sheet Molding Compound (A-SMC) composite materials. Multi-scale damage modelling based on the Mori-Tanaka approach is put forward. Previously, the results of an experimental campaign carried out on a range of strain rates varying from quasi static to 200 s−1 were used to identify a probabilistic local damage criterion based on Weibull’s formulation and integrate the effect of damage at a fiber-matrix interface scale. Therefore, the progressive local damage occurring under a fast loading may be described. A two-step homogenization procedure allows describing the strain rate effect on the stress-strain curves. The model gives also rise to the prediction of the progressive anisotropic loss of stiffness. Comparing between the experimental and numerical results confirms the ability of the proposed approach to describe the visco-damage effect (delay of damage threshold and decrease in damage kinetics) emphasized in A-SMC composites.