This paper presents an incremental analytical model for theoretically predicting the strain hardening hysteretic behaviour of a steel brace member subjected to cyclic loading. The model consists of a pin-ended bracing member with a plastic hinge at midspan. Braces with other end conditions are handled using the effective length concept. An incremental solution procedure is herein employed where the incremental axial force dP is related to the incremental axial deformation dδ by means of a tangent stiffness coefficient Kt. Stepwise regression analysis is used to approximate the plastic conditions for the steel Universal Column (UC) section. Different cross section shapes of a bracing member can be accounted for by specifying the different yield surface approximations. Several simple one-surface type hardening rules are employed to evaluate the effect on the analytical prediction of a steel bracing cyclic behaviour. The analytical results are compared with available experimental data on actual brace members, confirming the validity of the analytical model developed for practical use. The proposed model has been incorporated into an inelastic dynamic frame analysis program to evaluate the inelastic seismic response of the braced steel structures. © 1997 Elsevier Science Ltd.