The lateral stiffness of CFT beam-columns is considered to decrease because of the damage by the concrete crack or yielding of the materials however the relationship between two phenomena is not clear. It is necessary to clarify the strength when the CFT columns damaged by the concrete crack for evaluating the lateral stiffness of CFT beam-columns properly. The purposes of this study are to calculate the flexural crack strength of a square CFT section and to compare them with the yield strength. The analysis is carried out as follows; 1) assuming the stress-strain relationships of materials and the strain and stress distribution of the cross-section, 2) setting the limit of the tensile strain of concrete and 3) calculating the relation between the axial force and the bending moment when the strain of concrete reaches the limit tensile strain. Parameters are width-thickness ratio, the yield strength of a steel tube and compressive strength of concrete. As a result of the analysis, we showed that the axial force ratio is 0.2 ~0.3 when the flexural crack strength and the yield strength are the same. It is concluded that the lateral stiffness decreases because of the crack of concrete - and not from the yielding of materials -- when the axial force ratio is smaller than 0.2~0.3.