Main purpose of this paper is to describe the relationship between slenderness ratio of the steel brace in the Buckling Restrained Brace (BRB) and stiffness of the cover. For the objective, contact analysis of the finite element method is applied to deal with behavior of the steel brace such as transition of mode from lower to higher-order mode. Several examples of the BRB, of which slenderness ratio distributes from 135 to 360, are analyzed. The obtained results are verified through actual experiments. Based on the obtained minimum required stiffness of the covers, relationship between the slenderness ratio of the steel brace and the strength of the cover is analytically formulated.