The principal stress based evolutionary structural optimisation method is presented herein for topology optimisation of arch, tied arch, cable-stayed and suspension bridges with both stress and displacement constraints. Two performance index formulas are developed to determine the efficiency of the topology design. A refined mesh scheme is proposed to improve the details of the final topology without resorting to the complete analysis of a finer mesh. Furthermore, cable-supported bridges are optimised with frequency constraint incorporating the "nibbling" technique. The applicability, simplicity and effectiveness of the method are demonstrated through the topology optimisation of the four types of bridges.