To theoretically analyze the elastic lateral-resistant stiffness of corrugated steel plate shear walls, the relationship between elastic modulus, shear modulus, and unknown Poisson’s ratio of corrugated steel plates with different wave forms was obtained by comparatively analyzing the in-plane deformation of equivalent orthotropic plate under pure shear and pure principal stress in elasticity phase using orthotropic plate theory. The unknown Poisson’s ratio was calculated inversely by shear modulus of steel plate to obtain the unified formula of shear modulus for corrugated steel plates. Applying the unified formula to the elastic lateral stiffness formula of thick steel plates, the elastic lateral stiffness formula of corrugated steel plates was obtained. The elastic lateral-resistant stiffness of corrugated steel plate shear walls was calculated by simple addition of corrugated steel plate stiffness and frame stiffness. The reliability of the proposed formula was verified by existing shear modulus formula of corrugated steel plates. Then, a total of 70 models were simulated based on ABAQUS finite element analysis software for corrugated steel plate shear walls with different wave forms and sizes to verify the uniformity of the proposed formula. Results show that the unified formula was accurate and reliable for calculating the elastic lateral-resistant stiffness of corrugated steel plate shear walls. The wavelength and corrugation expansion length both had significant effects on the elastic lateral-resistant stiffness, while the wave forms of corrugated steel plates had no effect on the variation of elastic lateral-resistant stiffness when the wavelength and corrugation expansion length were constant. Finally, the application scope of the unified formula was determined.