An elastic-plastic finite element method (FEM) is used to analyze the stress distributions ahead of crack tips for three types of COD specimens with different precracked depth a/W and height W of a low alloy steel, and the tensile and COD tests are carried out at various temperatures. By accurately measuring the distances of the cleavage initiation sites from the blunted crack tips, the local cleavage fracture stresses σf are measured. With increasing precrack depth a/W, specimen height W and test temperatures in a certain range, it was found that the σf essentially does not change. The σf is a steady inherent parameter of the material whose value is independent of the precracked specimen geometry.