In recent years there has been a growing interest worldwide in stress based topology optimization which aims at achieving least weight and more uniformly stressed designs. This paper presents the optimum topology design of arch, tied arch and cable-stayed bridges by means of the evolutionary structural optimization method (ESO). This can be accomplished by employing the evolutionary optimization scheme incorporating the principal stress criteria, thereby utilizing the available tensile and compressive materials more effectively. In addition to the stress constraint, the displacement constraint is also considered in the optimization process. Two performance index formulae have been proposed for tension- and compression-dominant designs based on the element stresses. They can be used effectively to reflect the variations of the maximum principal stresses and the design volume during the evolutionary process, hence indicating the optimum topology for the final design. The optimum designs of the aforementioned three types of bridges are investigated under various loading conditions. Further, comparisons are made between each individual design for a certain type of bridge and the performance of the design is also examined.