There is an increasing demand in carbon fibre reinforced (CFR) composites primarily due to their high strength-to-weight ratio. Although their single-ply behaviour is rather brittle (as compared to metals), by reducing the ply thickness and stacking differently oriented plies, brittleness is suppressed, and a ductile behaviour similar to metals is achieved. In this thesis, a recently proposed material model inspired by crystal plasticity is reconsidered and implemented in an implicit finite element solution framework. To this end, a user-defined element is developed in a geometrically non-linear continuum setting and implemented in commercial finite element software Abaqus through UEL (Userdefined ELement) subroutine. The model is validated by analytical solutions derived for simple shear cases and two experiments for different loading cases from the literature. The model is capable of predicting stress-strain response well in cases where matrix plasticity is dominant. Moreover, a parametric study on the cross-ply shear specimen is conducted to investigate the influence of different material parameters. In the last part, the model is extended by a continuum scale damage in the matrix and degradation in elastic material properties. The predictive capabilities of the damage extended model are assessed by re-analyzing the cross-ply shear test.