- Analytical solutions of a general third-order plate theory that accounts for the power-law distribution of two materials through thickness and microstructure-dependent size effects are presented. The Navier solution technique is adopted to derive analytical solutions to simply supported rectangular plates. The modulus of elasticity and the mass density are assumed to vary only through thickness of plate and a single material length scale parameter of a modified couple stress theory captures the microstructure-dependent size effects. Examples of bending, buckling, and vibration problems are presented to show effects of the power-law distribution of two materials and the microstructure-dependent size parameter. 2013 Elsevier Ltd.