Abstract: The structural behavior of the core component is one of the key factors that influence the low-cycle fatigue and hysteretic character of buckling-restrained brace (BRB). Based on the structural features of the BRB, some basic assumptions are introduced to establish the equilibrium equation of a member subjected to axial and lateral force. Equations are then derived to describe the deflection curve of the core component under the situation of point contact and line contact. The multi-wave buckling process of the core under increasing axial load in turn of point contact, line contact and generation of new wave is revealed. A calculation example illustrates that the derived equations agree well with the numerical results, and the equations can be used to describe the structural behavior of the BRB core.