This paper deals with the modelling of damageable viscous behaviour of short-fibre reinforced composites (SFRC) with complex distributions of fibre orientations and for a wide range of strain rate. In the present model, the composite material is seen as the assembly of a matrix medium and several linear elastic fibre media. Then, the computation of composite macroscopic behaviour is based on an additive decomposition of the composite state potential into potentials of different media. The matrix behaviour is modelled as strain-rate sensitive, i.e. viscoelastic (VE) and/or viscoplastic (VP), and an anisotropic ductile damage model is coupled to matrix VE-VP constitutive laws. Fibre matrix interfacial degradation is also modelled through the degradation of load transmission from matrix to fibres as soon as microcracks are initiated at fibre tips and propagate along fibre sides. The accuracy of both damage laws coupled to the strain-rate dependent behaviour model of composite material is validated based on comparisons with experimental data obtained for a PP matrix reinforced with short glass fibres. These comparisons are performed at different loading rates and different loading angles with respect to the fibres’ preferential direction of orientation induced by injection moulding process.