Energy release rate for cracks in finite strain elasticity Griffiths fracture criterion describes in a quasistatic setting whether or not a pre existing crack in an elastic body is stationary for given external forces. In terms of the energy release rate (ERR) which is the derivative of the deformation energy of the body with respect to a virtual crack extension this criterion reads: If the ERR is less than a specific constant then the crack is stationary otherwise it will grow. In this paper we consider geometrically nonlinear elastic models with polyconvex energy densities and prove that the ERR is well defined. Moreover without making any assumption on the smoothness of minimizers we derive rigorously the well known Griffith formula and the $J$ integral from which the ERR can be calculated. The proofs are based on a weak convergence result for Eshelby tensors.