We consider a nonlocal fracture model and study the convergence properties of the finite element and the finite difference approximation. The model is a nonlinear state-based peridynamic model. We show the well-posedness of the model and show a priori convergence rate for the finite element and the finite difference approximation. We perform numerical experiments with fracture and numerically compute the rate of convergence. We show the good agreement between theoretical convergence rate and numerically computed convergence rate. The peridynamic model is designed such that the nonlocal fracture energy and the classical Griffith’s fracture energy agree for any given size of horizon. This is demonstrated through numerical examples.