In this study, numerical procedures for thee-dimensional elastic-plastic X-FEM analysis including selections of the near-tip enrichment functions are examined. The utilized enrichment functions approximate the asymptotic displacement field near the crack tip obtained by the HRR solution. As a numerical example, a surface crack problem of elastic-plastic materials is solved to evaluate the crack opening displacement and the J-integrals along the crack front, which is evaluated using the domain integral method. Obtained results are compared with those obtained using conventional finite element analysis.