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A line integral is exhibited which has the same value for all paths surrounding the tip of crack in a two dimensional strain field of elastic-plasticc material. Finite element method was used to determine Rice's J-integral value in centrally cracked plate. These numerical J-integral values were compared with corresponding values of reference with low hardening and high yield strength. The J-integral value was also computed for a crack extension and different load condition. For increasing crack length the value of J-integral also increases, this means that the crack is unstable. To prove path independent, three paths were used in the analysis and proved