This paper presents a Fourier-related double scale analysis to study the instability phenomena of sandwich plates. By expanding the displacement field into Fourier series, the sandwich plate model proposed by Yu et al. (2015), using the classical plate theory in the skins and high-order kinematics in the core, is transformed into a new Fourier-based reduced two-dimensional sandwich plate model with the slowly varying Fourier coefficients as macroscopic unknowns. The resulting nonlinear equations are solved by the Asymptotic Numerical Method (ANM), which is very efficient and reliable to capture the bifurcation point and the post-buckling path in wrinkling analyses. Both antisymmetrical and symmetrical wrinkling for sandwich plates under uni-axial and equi-biaxial compressive loads are studied and the numerical results demonstrate that the Fourier-based finite element model can accurately yet efficiently predict wrinkling patterns and critical loads, especially when dealing with wrinkling phenomena with extremely large wavenumbers.