Abstract: By coupling natural boundary element method (NBEM) with FEM based on domain decomposition, the torsion problem of the square cross-sections bar with cracks have been studied, the stresses of the nodes of the cross-sections and the stress intensity factors have been calculated, and some distribution pictures of the stresses have been drawn. During computing, the effect of the relaxed factors to the convergence speed of the iterative method has been discussed. The results of the computation have confirmed the advantages of the NBEM and its coupling with the FEM.