In this paper, the crack tip stress method (CTSM), which is the method for accurately calculating the stress intensity factors based on the usefulness of the stress values at a crack tip calculated by the finite element method (FEM), is extended to the tensile problems of the bi-material cylinder. In order to investigate the differences of the stress states between the bi-material cylinder and the bi-material plate, FEM analyses are performed on them under the same material combinations and the same mesh patterns. The asymptotic solution of the cylinder is derived from the FEM analysis results, and the boundary conditions such as the traction-free surface and the perfectly boned interface. Analyses of the intensity of the singular stress field are performed on the various bi-materials which have the same Dundurs' parameter by using the bi-material plate subjected to the tensile stress under the plane strain as the reference model.