This paper presents an analytical solution of the linear buckling, free vibration and bending behavior of simple supported functionally graded sandwich plates subjected to transverse and axial mechanical loads. The used optimization strategy allows to express the transverse and in-plane displacement fields as a function of the n and m parameter, respectively, so the used Carrera's unified formulation (CUF) is also n and m parameters dependent. Principle of virtual displacement (PVD) is utilized to obtain the highly coupled differential equations. The solution is obtained via Navier-Type solution. Good agreements with quasi-3D solutions are found. The optimized parameters are used for solving the buckling problem of functionally graded sandwich plates with different side-to-thickness ratios. Numerical results for buckling are compared to different advanced theories since there isn't 3D solution available in the literature. Overall, the presented results have a high accuracy to estimate the critical loads, modes and natural frequencies.