In this paper a general expression of the potential energy release rate G for a three-dimensional fracture mechanics problem is supplied. Under the hypothesis of a quasi-static growth phenomenon, the distribution of the vector a, i.e. the velocity field of the fracture propagation, is assumed unknown along the crack front. This assumption leads to a general formula of G for a three-dimensional hyperelastic body containing a plane crack. Moreover, imposing a stationary condition of G with respect to a, the analytical problem of the crack front shape evaluation is formulated. A unique solution exists for the problem, which is described by a system of two non-linear equations. Practical applications of the theory can be obtained by the use of finite element analysis results, together with a numerical solution of the two equations in the unknown components of the fracture propagation velocity.