In this paper, we develop new asymptotic path-independent integrals for the evaluation of the crack tip parameters in a 2D neo-Hookean material. The new integrals are of both J-integral and interaction energy integral type and rely on the separation of the asymptotic boundary value problem into independent problems for each of the deformed coordinates. Both the plane stress and plane strain cases are considered. The integrals developed are used to compute the amplitude parameters of the asymptotic crack tip fields, which allows for direct extraction of these parameters from numerical results. A long strip with an edge crack under mixed loading modes is considered for both homogeneous and biomaterial cases. It is found that the asymptotic J-integrals produce good results for the first-order parameters while the interactions integrals produce good results for both the first and second-order parameters.