To improve the elastic shear buckling strength (ESBS) of variable cross-section corrugated steel webs (CSWs) while controlling engineering cost (EC), this study optimizes the web geometry of a continuous rigid frame bridge with CSWs of variable cross-section. First, finite element analysis (FEA) models of CSWs with different geometric parameters were established. The relationships between web dimensions and ESBS were obtained through response surface fitting, while the relationships between geometric parameters and EC were calculated using the slicing method. Second, the Pareto optimal solution set was derived using the NSGA-Ⅱ algorithm. The combined weight of the optimization objectives was determined by integrating the expert scoring method, the entropy weight method, and the minimum deviation principle, and the optimal scheme was selected using the technique for order preference by similarity to ideal solution (TOPSIS). Finally, the impact of parameter variations on the optimization results was analyzed. The results verify that the established FEA model and fitting formula are accurate and effective through buckling mode validation and response surface significance tests. Compared with the original design, the optimal scheme increases the ESBS by 93.5% and the EC by 37.1%. Some Pareto solutions outperform the original design in both indicators, indicating potential for improvement in the original dimensions. According to the response surface fitting formula, ESBS increases with larger wave height, plate thickness, and short-side height, but decreases with larger flat strip width and long-side height. The subjective weighting significantly affects the final scheme selection: as the subjective weight of ESBS increases, both ESBS and EC in the optimal scheme rise accordingly.