The finite element alternating method (FEAM) was extended to obtain fracture mechanics parameters and elasto-plastic stress fields for 3-D inner cracks. For solving a problem of a 3-D finite body with cracks, the FEAM alternates independently the finite element method (FEM) solution for the uncracked body and the solution for the crack in an infinite body. As the required solution for a crack in an infinite body, the symmetric Galerkin boundary element method formulated by Li and Mear was used. For elasto-plastic numerical analysis, the initial stress method proposed by Zienkiewicz and co-workers and the iteration procedure proposed by Nikishkov and Atluri were used after modification. The extended FEAM was examined through comparing with the results of commercial FEM program for several example 3-D crack problems.