A new path independent integral that represents the rate of energy flux at the tip during crack extension in a homogeneous and isotropic material has been derived from the principle of virtual work for a two-dimensional stationary circular arc crack subjected to multiple loads under static conditions. Again considering appropriate energy balance law, another new path area form of integral has been formulated for the similar circular arc crack geometry subjected to rapidly varying loads. In the absence of inertia effects equals and they include the presence of the effects of thermal strains, initial strains and body forces. It has been further demonstrated that the integrals are generalized forms of several other available path independent integrals including Rice’s J-integral. *FJFJˆ FJˆ*FJ The integrals have been implemented into a finite element post-processing program for examining the path independence behavior under elastic and elastic-plastic deformation subjected to mechanical and pure thermal loads. Initially, the mesh convergence studies have been performed to establish the solution accuracy. An approach for computing these integrals in the finite element context has been proposed and the invariant property of these integrals computed on several contours has been examined under different types of working loads. The initial part of the investigation refers to the elastic and incremental elastic-plastic analyses under mechanical loads while in the next part; the invariant property under thermal loads has been examined. Numerical results demonstrate that the path independence is well preserved over the integration contours for both the load cases within the limits of computational accuracy.