The classical Euler-Bernoulli girder theory is not applicable due to shear deformation of corrugated steel web, elastic bending theory considering shear deformation is presented to analyze deflection and mechanical property. Differential equation is derived based on displacement field assumption, internal force equilibrium equations, deformation compatibility condition and relation of deformation and internal force, and solutions are obtained according to boundary and load condition. Simply supported I and box girder bridges with corrugated steel web are analyzed with elastic bending theory considering shear deformation, their predicted results are found in good agreement with those by 3D finite element analysis and test. A limit value of depth-span ratio is suggested for considering influence of shear deformation or not, the simplified formula of deflection in middle span is presented to guide deflection design. Corrugated web accounts for more than 80% of total shear force in the whole span under uniform load while one third apart from bearing under concentrated load in mid-span. The elastic bending theory considering shear deformation makes a reference for designing composite bridge with corrugated steel web.