The bearing forced displacement method is a widely used control method in the closure construction of steel girder bridges. However, the theoretical research on the construction process of the bearing forced displacement method still needs to be completed. In this paper, based on the differential equation of Euler beam deflection, the integral method is used to solve the flexural closure solution of a three-span continuous girder in two conditions, namely, the bridge completion and closure in stages and the one-time bridge completion. The beam deflection functions obtained in both conditions are identical, which proves that the ideal one-time bridge formation can be achieved by applying the bearing forced displacement method. Finally, with a closure construction application of a three-span continuous steel truss bridge, the applicability of the forced displacement method in bridge alignment control applications is verified. The theoretical proof can provide a theoretical basis and technical reference for the engineering application and promotion of the bearing forced displacement method.