Meshing gear pairs have regions of high stress gradients due to contact loading. In other applications, high stress gradients can also be generated due to geometric irregularities, material mismatch, or thermal mismatch. In meshing gear pairs, the extent of the region with a high stress gradient depends on the material and the geometric properties. It is common that failure, through crack initiation, will occur in the region of high stress and strain gradients. The conventional Weibull failure theory fails to accurately predict the probability of failure of components with high stress gradients. In this research, the contact loading in a gear pair, with asymmetric teeth, is analyzed. Thus, the objective of this work is to develop a Weibull failure theory to handle the high stress gradients due to contact loading in gear pairs with asymmetric teeth. The modified Weibull failure theory developed uses the weight function approach to account for the variation of the critical stress along the face of natural flaws. For contacting gear teeth, it is demonstrated that the modified Weibull failure theory generates monotonous trends for the probability of failure with respect to increasing Weibull modulus.