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This contribution focuses on gradient formulations for the prediction of the static failure load of V-notched and cracked components made of brittle materials. A weighted average of the local equivalent stress, called non-local equivalent stress, is first considered and subsequently approximated by a gradient expansion up to the spatial second-order derivative. A distinguishing characteristic of the present approach is that the non-local equivalent stress is calculated by solving a differential equation of implicit type. The numerical solution for a V-notch in the presence of Neumann’s boundary conditions is presented. Moreover, the analytical solutions of an one-dimensional case is proposed. Finally, the static failure loads predicted by to the present formulation through the finite element technique are compared with the experimentally determined ones.