Although there are several criteria for mixed mode brittle fracture, to the authors’ knowledge, there is no generally accepted model for predicting the probability of elastic fracture (cumulative probability function,  under mixed-modes I and II loading. This paper employs a probabilistic approach and proposes a pragmatic and relatively accurate model based on the concept that the damage  at the crack-tip depends on intensities of the general and hydrostatic strain energy densities in the vicinity of the crack-tip as well as the relative amount of mode I to mode II loading defined by a mode-mixity parameter  The model then postulates that the artificial neural network can be used to establish the relationship between  D and b. The application of the proposed model to PMMA (a polymer) and En3B mild steel (a metallic alloy) at -  show that the mixed modes I and II probability of fracture can be predicted with the mean squared error (MSE) as low as 0.06.