In this study we simulate the fatigue test of a compact tension specimen and obtain the displacements, stresses and strains by using the finite element method. And we examine the path independency of $Delta$J integral values and compare it with $Delta$J integral values calculated from load-load line displacement curve. From the results of this study, we can find that $Delta$J integral show the path Independency for saturated materials. We can also find that the path independency of $Delta$J Is not satisfied when different material Is assumed near the crack tip, but the difference in $Delta$J is small. And $Delta$J integral values calculated from load-load line displacement is very analogous with those from integration path but always have lower values than those from integration paths. In the case of crack closing, we found that $Delta$J integral values from load-load line displacement should be calculated with the load Increment values based on the crack opening point. The unsaturated material is also simulated and its $Delta$J shows different values according to the path, but the difference is small.