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Peridynamics (PD) represents a new approach for modelling fracture mechanics, where a continuum domain is modelled through particles connected via physical bonds. This formulation allows us to model crack initiation, propagation, branching and coalescence without special assumptions. Up to date, anisotropic materials were modelled in the PD framework as different isotropic materials (for instance, fibre and matrix of a composite laminate), where the stiffness of the bond depends on its orientation. A non-ordinary state-based formulation will enable the modelling of generally anisotropic materials, where the material properties are directly embedded in the formulation. Other material models include rocks, concrete and biomaterials such as bones. In this paper, we implemented this model and validated it for anisotropic composite materials. A composite damage criterion has been employed to model the crack propagation behaviour. Several numerical examples have been used to validate the approach, and compared to other benchmark solution from the finite element method (FEM) and experimental results when available.