Variable thickness plates are commonly encountered in the majority of mechanical/structural components of industrial applications. And, as a result of the unsymmetry of the structure or the load and the anisoptropy of the materials, the cracks in engineering structures are generally subjected to combined stresses. In spite of considerable practical interest., however, a few fracture mechanics study on combined mode crack in a variable thickness plate have carried out. In this respect, combined mode I/III stress intensity factors K₁ and K_m at the crack tip for a variable thickness plate were obtained by 3-dimensional finite element analysis. Variable thickness plates containing a central slant crack were chosen. The parameters used in this, study were dimensionless crack length λ, crack slant angle α, thickness ratio β and width ratio ω. Stress intensity factors were calculated by crack opening displacement(COD) and crack tearing displacement(CTD) method.