The path independency of J-integral proposed by Rice has been accepted to be valid in both linear and nonlinear elastic materials. This independency, however, has not been necessarily proven for incremental elasto-plastic materials.In this paper, at first, FEM analyses based on deformation and incremental plasticity theories were performed in order to compare the solutions obtained through these two theories. Some factors governing the path independency of J-integral were examined with an emphasis on the loading condition of an element in the vicinity of crack tip. From the analyses and examinations, the applicability of J-integral according to the incremental plasticity theory was clarified.Next, the results of FEM analyses based on the incremental plasticity theory were investigated to verify the adequacy of analytical assumptions employed to develope suitable formulas estimating J-values from a single load-displacement curve. The applicability and limitation of these formulas were confirmed and advanced. As a consequence of these studies, a new formula which is a modification of Rice's estimation procedure was proposed.