Within the framework of re-modified couple stress theory, the Refined Zigzag Theory is added to the vibration and buckling analysis of sandwich micro-plates embedding functionally graded layers. The disparity between the scale effects along two orthogonal directions is considered through two orthogonal material length scale parameters (MLSPs). Meanwhile, the solutions of natural frequencies and buckling loads show an improved predictive capability through comparing the results with exact and quasi-3D solutions. Two types of functionally graded sandwich micro-plates with simply supported boundary conditions are taken as the illustrative examples, namely, an isotropic functionally grade sandwich micro-plate with a power law and an orthotropic one with an exponential law. The numerical results indicate that the present model can capture the varying scale effects along two orthogonal directions, particularly when the geometric size of the micro-plates is comparable to the MLSPs. When microscopic isotropy is observed, the present model can also make accurate predictions on those kinds of micro-structures by setting the two orthogonal MLSPs equal to each other. In addition, the scale effects are less obvious as the functionally graded sandwich micro-plate is getting thinner and harder; the grading index also has an influence on the scale effects, but this influence is simultaneously depending on the side-to-thickness ratio of the micro-plate.
