A high stress gradient occurs in a component when the stress, due to external loading, rises asymptotically. The Weibull failure theory overestimates the probability of failure for components with high stress gradients generated due to the geometric irregularities, material mismatch, thermal mismatch, and contact loading. A modified Weibull failure theory is proposed in this paper. The method is based on the weight function method. The modified Weibull failure theory was applied to two specimens, and the results showed the ability of the proposed theory to handle high stress gradients. The theory considers variable equivalent stress intensity factors along the faces of cracks; hence, it considers the strength of a specimen to be dependent on the stress field.