The bi-periodic trapezoidal corrugated plate is a new type of lightweight structure with periodic trapezoidal corrugated changes along two plane directions. At present, there is little research on the relationship between its mechanical properties and structural parameters, limiting the popularization and application of this structure. In this article, a numerical model of the represent element (or called unit cell) is established by using the variational asymptotic method to calculate the equivalent stiffness. Then, the bi-periodic trapezoidal corrugated plate is converted to orthotropic plate with the same stiffness characteristics by homogenization technology. Based on this method, the equivalent stiffness with different structural parameters, global deformation and buckling modes are calculated, and the accuracy of the equivalent model is verified by comparing with the three-dimensional finite element simulation results. The results show that the equivalent stiffness of the bi-periodic trapezoidal corrugated plate is lower than that of the plate due to the change of the shape, and the bending stiffness is increased. The tensile stiffness increase and the bending stiffness decrease with increasing interval length and decreasing plate height. While with the increase of plate thickness and web length, the bending stiffness shows an upward trend. The constructed model is suitable for the case that the period of corrugation is far less than the structure size. The approximate energy of the equivalent plate model is as close as that of the original three-dimensional corrugation plate, which is guaranteed by the asymptotic expansion analysis of the leading terms of energy functional. The equivalent plate model can be used to calculate the equivalent bending moment and the equivalent maximum tensile/compressive stress of corrugated plates with different material properties, which can effectively reduce the calculation amount and save the calculation resources.