Aluminum alloy tubes are widely used in various industries because of their excellent performance. Up to now, when the tube is bent, the elastoplastic deformation evolution mechanism of the cross-section has not been clear, and no direct analytical proof has been found. In this paper, based on the bilinear material model assumption, a new mechanical model of tube plane bending deformation is constructed. The analytical model can describe in detail the evolution mechanism of elastic–plastic deformation on the cross-section of the tube after bending deformation, the position of the elastic–plastic boundary, the position of the radius of the strain neutral layer, and the relationship between the bending moment over the section and the bending radius. According to this model, the deformation law of the tube cross-section during bending is elucidated. The results are as follows: (1) the deformation evolution of the cross-section of the bending deformed tube calculated by the analytical model is in good agreement with the finite element model (FEM) of pure bending. (2) By comparing the results of the analytical model with FEM results, and the processing test of the self-designed four-axis free bending forming tube bender, the bending moments are in good agreement. (3) Compared with the bending moments calculated by several other analytical models of tube bending, this model has a relatively small deviation value.