It has been a great challenge for many scientists and engineers to compute elastic-plastic solutions for dynamically loaded cracked structures due to the fact that the solutions are much more complicated and computationally time consuming than corresponding static problems. The path independent integral J^F, originally developed for a two-dimensional dynamically loaded stationary circular arc crack in a homogeneous and isotropic material, is evaluated in the present study by taking elastic-plastic material properties to quantify the crack problem. All the numerical results presented in this study were evaluated using general purpose finite element commercial software ANSYS together with the post-processing program (using FORTRAN) developed by the authors. Numerical results thus obtained are compared with good agreement within the limits of computational accuracy and the path invariant property of J^ F is well preserved over the integration contours. © 2013 Elsevier B.V.