Prefabricated corrugated-steel-plate (CSP) structures have been increasingly applied in tunnel maintenance. In practice, the varying stiffness of bolted joints can change their mechanical characteristics and failure mechanism. This paper presents experimental and numerical investigations of the joint behavior and bending resistance of CSP flange joints under combined compression and bending forces. Full-scale tests were conducted on CSP flange joints with and without axial forces, and the deformation characteristics and failure modes were analyzed and discussed. Numerical simulations were then conducted to simulate the test joint responses and applied to conduct parametric studies. The influence of the axial force, CSP thickness, flange plate thickness, and bolt preload on bending performance was evaluated based on the test and numerical data. The results revealed that the flange joint specimen under combined axial and bending load exhibited superior integrity, less flange plate deformation, and less vertical midspan displacement, compared with the pure bending condition. An increase in the axial force, CSP thickness, and flange plate thickness greatly improved the bending stiffness of the joint, with the flange plate thickness having the greatest effect and the bolt preload having no obvious effect on the bending performance. Comprehensive structural economy and safety considerations suggested that the CSP thickness should exceed 6 mm and the flange plate thickness should be between 10 and 15 mm. Additionally, for practical purposes, a backpropagation neural network was developed. The proposed neural network model accurately and effectively predicted the joint rotation angle using the joint geometric parameters and load conditions. This paper provides a reference for the flange-joint design of corrugated-steel structures.