The response of continuous curved box girder with corrugated steel webs is rather complicated due to the coupling effect of bending and torsion. In order to study the mechanical properties of continuous curved box girder with corrugated steel webs, considering the effect of shear lag and shear deformation, the restrained torsion differential equation of simply supported statically indeterminate curved box girder with corrugated steel webs (CCBG(CSWs)) are derived based on the energy method, and then analyzed and verified by combining CCBG(CSWS) simply-supported structure, using the differential equation combined with the three-bending moment method to solve the internal force of a three-span continuous curved box girder with corrugated steel webs, and the results are compared with those of the curved bar structure mechanics method and of the finite element analysis. The results show that: considering the effect of shear lag and shear deformation, the internal force results obtained by the method proposed in this paper are in good agreement with those obtained by finite element method, which verifies the correctness of the method proposed. The shear lag effect and shear deformation have a certain influence on the internal forces of CCBG(CSWS), and the influence on the internal forces of multi-span CCBG(CSWS) structure is more obvious.