This study presents a data-driven, probability embedded approach for the failure prediction of IM7/8552 unidirectional carbon fibre reinforced polymer (CFRP) composite materials under biaxial stress states based on micromechanical modelling and artificial neural networks (ANNs). High-fidelity 3D representative volume element (RVE) finite element models were used for the generation of failure points. Fibre failure and the friction between fibres and matrix after fibre/matrix debonding were taken into consideration and implemented as VUMAT subroutines, respectively. Uncertainty quantification was conducted based on a coupled experimental-numerical approach and failure probabilities were inserted into the failure points to generate the database for the training of ANNs. A total of 15 biaxial stress combinations were considered for the generation of datasets. Two strategies were considered for the construction of form-free failure criteria based on the ANNs for regression and classification problems. It is found that for the regression problems, an ANN model with 2 hidden layers and 64 neurons can achieve a mean square error (MSE) of 0.027% and a mean absolute error (MAE) of 0.78%. For the classification problems, an ANN model with 3 hidden layers and 32 neurons, presents an excellent performance in the prediction with a probability of 98.1%. A good agreement was observed between the failure strength of composites under transverse and in-plane shear predicted by these ANNs and failure envelopes theoretically predicted by Tsai–Wu and Hashin failure criteria.