Inter-fibre failure analysis of carbon fibre-reinforced polymer (CFRP) composites, under biaxial loading conditions, has been a longstanding challenge and is addressed in this study. Biaxial failure analysis of IM7/8552 CFRP unidirectional (UD) composites is conducted under various stress states. Two widely accepted failure criteria, the interactive Tsai-Wu and non-interactive Hashin failure criteria, are comprehensively assessed with finite element-based micromechanical analysis. High-fidelity three-dimensional representative volume elements (RVEs) are subjected to biaxial loadings with imposed periodic boundary conditions. Carbon fibres are assumed to be transversely isotropic and linearly elastic. The Drucker-Prager plastic damage constitutive model and cohesive zone model are utilised to simulate the mechanical response of the matrix and fibre-matrix interface, respectively. Coulomb friction is assumed between the fibres and matrix after interface failure. Two sets of biaxial loading scenarios (i.e. transverse stress dominated and shear stress dominated) with the associated failure modes are selected for the failure analysis and assessment of these failure criteria. A data-driven failure envelope for the composites under biaxial loadings is developed using a univariate cubic spline function. Failure mode transition points are determined under biaxial loadings. It is found that the micromechanics-based numerical model is effective in assessing these two existing criteria.