In the previous papers, the authors proposed the β-value as the constraint coefficient due to the plate thickness. The purposes of this paper to find analytically the relation between the β-value and thickness B and to evaluate the J_c -value and critical COD, φ_{0 c} for any thickness specimen by using the β- B relation, respectively. Stress distributions in the thickness direction are estimated, using the results of calculation by the three dimensional elastic FEM and the Prantl's experimental data, to make a analysis of the relation between β and B . From this study, following conclusions are obtained : 1) The β-values evaluated by this analysis display good agreement with the experimental results shown in the previous paper. 2) It is expected that the J_c -value and φ_{0 c} for any thickness specimen are able to be calculated by formulas proposed this paper considering the thickness effects on the fracture toughness by using a known J_c -value and φ_{0 c} for a standard thickness specimen.