Manufacturing-induced defects, especially fibre waviness, are well known to substantially reduce the longitudinal compressive stiffness and strength of unidirectional (UD) composite materials. Nevertheless, the three-dimensional (3D) nature of fibre waviness and its effect on material performance have not been comprehensively investigated in the literature. In this work, a microscale model incorporating representative 3D fibre waviness extracted from CT images is developed to more accurately capture these manufacturing imperfections. The 3D waviness mode is generated by combining two basic two-dimensional (2D) waviness forms: a Snake-like pattern to describe in-plane fibre deviation, and a Bridge-like pattern to describe out-of-plane fibre undulation. Furthermore, individual 3D representative volume element (RVE) finite element models specifically featuring both the Snake-like and Bridge-like patterns are independently investigated to isolate their respective influences on mechanical degradation. Microscale RVE models encompassing the integrated 3D fibre waviness, alongside residual stresses arising from the fibre deformation, are constructed to simulate the longitudinal compressive response. The stiffness and strength predicted by these simulations show high correlation with experimental results. The comparisons indicate that under the coupling effect of waviness in two planes, both the compressive stiffness and strength of UD composite with 3D fibre waviness are significantly lower than those with 2D fibre waviness. Furthermore, progressive failure analysis reveals that the failure mechanism of UD composites with 3D fibre waviness involves the interaction of failure modes observed in 2D waviness. Crucially, the magnitude of the 2D feature angles dictates the ultimate failure characteristics of the 3D structure. This confirms that the proposed micromechanical modelling approach, with residual stress effects accounted for, can effectively capture the influence of complex 3D waviness on the longitudinal compressive behaviour of UD composites.