Additively Manufactured fibre reinforced components built via fused deposition modelling rapidly find applications within the European aerospace and transport industry, due to their well-known advantages, e.g., less machine, material, and labour costs, less manufacturing waste, and usage of more efficient materials. A drawback of additively manufactured components is their typically complex and in cases tessellated geometry; this gives rise to combined damage mechanisms (e.g., fibre pull-outs and matrix cracking) that deviate from the usual “high strength and ductile metal” paradigm. The phase-field method provides a robust damage modelling approach which is equipped with capabilities of automatically predicting initiation, propagation, branching and merging of complex curvilinear crack topologies. To this point, phase-field modelling has been widely applied to study brittle fractures based on Griffith’s theory, with extensions also to ductile and cohesive fractures. Composites are not brittle in the Griffith’s sense. Rather, they are prone to quasi-brittle damage modes wherein a crack is driven by cohesive forces present within the fracture process zone and develops along preferential crack directions due to the inherent anisotropy of the underlying domain. We present a cohesive phase-field model for simulating intra-laminar damage response in anisotrpopic 3D printed composites. The model employs a linear crack-surface density functional which retains a pure-elastic behaviour until damage onset, and a three-parameter quasi-quadratic degradation function which can be used to calibrate experimental strain softening curves, thereby accurately predicting quasi-brittle damage response in composites. The phase field model is examined within the context of 2D and 3D deformable domains. Acknowledgments: The second author gratefully acknowledges the support of the European Union's Horizon research and innovation programme under the Marie Sklodowska-Curie Individual Fellowship grant "AI2AM: Artificial Intelligence driven topology optimisation of Additively Manufactured Composite Components", No. 101021629.