The flat compression properties of corrugated sandwich structure are an important factor to evaluate their cushioning properties. At present, more research has been made on the mechanical properties in the cross direction (CD) and machine direction (MD), but less has been made in the flat compression direction. Selecting corrugated paperboards as samples, we analyzed the flat compression properties of the corrugated sandwich structure and explored the critical stress which is a key element for evaluating the cushioning properties based on theory and experiment. It is convenient to evaluate the cushioning properties and optimize the corrugated sandwich structure. Simplifying the corrugated structure into the struts, and referring to the bending theory of the standard beam theory, we explored the evaluating equation of the critical stress for corrugated sandwich structure by the bending moment and Euler formulas. The critical stress is in direct proportion to the elastic modulus and the thickness of the basis material. It is also closely related to the length of the corrugated cell-wall and the pasted width between the corrugated cell-wall and the linerboard. Changing the above parameters, we can change the compression resistance of the corrugated sandwich structure. The theoretical value of the critical stress of the corrugated sandwich structure is higher than the experimental value, since the mechanical properties are lost when the basis material is manufactured into corrugated sandwiches and corrugated boards. Therefore, the lost coefficient is introduced into the theoretic equation which can not only help optimize and design the corrugated sandwich structure, but also find application in optimized design of cushioning pads of corrugated sandwich structure.