The authors have proposed the buckling-restrained braces (BRBs) using steel mortar planks, providing stable hysteretic behavior under the high axial-strain conditions. The compressive strength of BRBs generally tends to be higher than the tensile strength.The authors understood that it was because of friction force between the surface of core plate and the restraining part, and that the magnitude of friction force was related to the buckling mode number resulting in the increase of contact points. A set of prediction formulas for the buckling mode number has been proposed in the authors� previous study. In this paper, the validity of the proposed formulas for the buckling mode number of plastic region of core plate is examined by the test results of strain gauge measurement on the core plate from the cyclically axial-loading tests. Furthermore, the relationship between the strength ratio of the compressive to tensile strength and the buckling mode number is evaluated. As a result, 1) the buckling mode number is approximately proportional to the slenderness ratio of the plastic region of core plate, and 2) the proposed formulas, considering the location of fixed point between the core plate and restraining part, correspond quite well to the test results in the relationship between the compression-to-tension strength ratio and the axial strain amplitude.