AbstractReissner’s principle (R-P), which considers the effect of all secondary shear stresses on shear deformation, is proposed for analyzing the elastic behavior of a composite box girder with corrugated steel webs (CBG-CSWs) under restrained torsion. The cross-sectional geometrical properties were calculated considering the accordion effect of corrugated steel web (CSW), and the formulas for warping normal stress and shear stress were derived. Based on this, the governing differential equation for restrained torsion of the CBG-CSWs was established based on R-P. In comparison with the widely used Umanskii’s second theory (U-ST), the expressions of the governing differential equation are the same, but the formulas for warping coefficient introduced in the derivation are different. A numerical simulation of the trapezoidal section simply supported girder was used to verify the effectiveness of the proposed theory. Comparing the stress results with three-dimensional finite-element (FE) confirms that the R-P is more accurate and suitable for analyzing the elastic torsion of the CBG-CSWs than U-ST. The warping coefficient calculated by U-ST is larger than that calculated by R-P, but it does not mean that the results of U-ST are favorable. The CSW is mainly subjected to torsional shear stress, whereas the bottom slab bears both warping normal stress and shear stress and attention should be paid to prevent oblique cracks. The variation of web thickness, width–span ratio, and height–span ratio also affect the restrained degree of sectional torsion, sectional geometric properties and stress results, which should be considered in the reasonable design of the CBG-CSWs. The influence of secondary shear stress on the total shear stress cannot be ignored. The proposed method based on beam theory avoids the complexity of the FE model development and solution, and its results can provide a reference for the restrained torsion analysis of the CBG-CSWs.