The X-FEM in conjunction with the level set method can be used to simplify the modeling of continua containing several cracks and hence perform effective stress analyses related to fracture mechanics. In this study, numerical procedures for elastic-plastic X-FEM analysis including selections of the near-tip enrichment functions are examined. As numerical examples, two-dimensional crack problems of elastic-plastic materials under plane strain condition are solved to evaluate the crack opening displacement and the J-integrals around the crack tip. Obtained results are compared with those obtained using conventional finite element analysis.