An adaptive finite element method for analyzing two-dimensional and axisymmetric nonlinear elastic fracture mechanics problems with cracks is presented. The J-integral is used as a parameter to characterize the severity of stresses and deformation near a crack tip. The domain integral technique is utilized as the J-integral solution scheme with the 9-node degenerated crack tip elements. The solution accuracy is further improved by incorporating an error estimation procedure to a remeshing algorithm with a solution mapping scheme to resume the analysis at a particular load level after the adaptive remeshing technique has been applied. Two benchmark problems are analyzed to evaluate the efficiency of the combined procedure.