This study deals with the modelling of the behaviour of laminated carbon/epoxy composites under static and fatigue loading. The non-linear cumulative damage model developed is written on the scale of the plies. It is based on a multi-criterion approach: brittle behaviour in the fibre direction, elastoplastic damage behaviour under shear and transverse tension stress, and elastoplastic behaviour under transverse compression loading. The range of validity of the model described here is limited to the first intra-laminar macro-crack, and it does not account for the delamination processes. This first-ply failure criteria model provides a conservative approach, which should be useful in some industrial context where the highest safety is required. Static tests results obtained on plate samples are presented [±45°]3s and hybrid glass/carbon [0,90]s are presented: they justify the modelling adopted here. The first tension/tension fatigue test results obtained on plate samples [±45°]3s are presented: they are used to identify the parameters of the model contributing to the shear behaviour.