To reduce investment cost and environmental impact of new civil engineering structures, an obvious approach is to reduce material usage. For bridge structures this poses a challenge, as demands put on the structure differ when analysing static and dynamic loading, with the end result being that bridge design is an iterative task. To address the problem, an optimisation procedure using a Genetic Algorithm (GA) is employed on a single span steel-concrete composite railway bridge, the Bryngeå Bridge on Botniabanan in northern Sweden. The optimisation is performed to obtain a lighter structure while still conforming to demands put on bridge structures presented in the Eurocodes. The criteria used in the work are quasistatic design calculations for the ultimate limit state, serviceability limit state and fatigue limit state, as well as a dynamic evaluation performed for train speeds up to 300 km/h, using the High Speed Load Models in the Eurocodes. In total, two optimisations are performed, one including retrofitted dampers on the bridge, and one exluding the dampers. The work is limited to minimising the mass of the steel girders in the bridge. Using accurate material parameters obtained from previous system identification of the bridge, results show that accelerations in conjunction with ultimate limit state loading limit the design of the bridge, and that I-girders with large tension flanges and small compression flanges produce the lightest cross-sections. Furthermore, results indicate that GA is an efficient tool for obtaining lighter structures.