[Purposes] The rigid-frame bridge is an important bridge type in modern bridge engineering and the reasonable selection of its cross-sectional dimension parameters has a significant impact on the structural response and stress conditions. This study aims to explore the sensitivity of the cross-sectional dimension parameters of the rigid-frame bridge to the key responses of the structure, and to clarify the influence degree of each parameter on the structural performance. [Methods] A long-span prestressed concrete continuous rigid-frame bridge was taken as the engineering background. Based on the response surface methodology (RSM), an explicit surrogate model was constructed between the key response of the structure (deflection and upper and lower edge stress) and the cross-sectional dimension parameters (main span height, root beam height, web thickness, and floor width). The sensitivity of each cross-sectional dimension parameter was thus systematically analyzed. The height of the box girder, the floor width, the web width and the roof thickness were selected as the design parameters. The vertical deflection of the end of the 8# segment (semi-cantilever), the mid-span deflection and the stress of the upper and lower edges after the bridge completion were taken as the response indexes. The central composite design (CCD) method was used to generate the parameter sample points, and the response data were obtained by combining the Midas finite element model analysis. The significance of the influence of each parameter on the structural performance was then quantified. [Findings] The web thickness is an important parameter among all four structural response indexes, with a sensitivity percentage between 96.66% and 97.98%. The other design parameters contribute less than 5% in the structural response, making them negligible parameters. [Conclusions] In the given design space and deviation range, when the cross-sectional dimension of the rigid-frame bridge changes, the web thickness becomes the main influencing factor for the deflection of the end during the construction process as well as the deflection and stress of the mid-span of the completed bridge.