The aim of this paper is to analyse the static behaviour of homogeneous as well as FGM (functionally graded material) thin micro/nano magneto-electro-elastic plates subjected to transversal static loading. within the higher-grade continuum theory of elasticity. The microscopic structure of material is reflected in this higher-grade continuum theory via one material coefficient called the micro-length scale parameter. Furthermore the material can be composed of two micro-constituents what is included in the employed continuum model by functional gradation of the material parameters through the plate thickness with assuming power-law dependence of volume fractions of micro-constituents on the transversal coordinate. The high order derivatives of field variables are eliminated by decomposing the original governing partial differential equations (PDE) into the system of PDEs with lower order derivatives. For the numerical implementation the novel Moving Finite Element approximation method is utilized. Several numerical simulations are devoted to study the influence of micro-length scale parameter as well as the parameters of gradation of material parameters on coupled bending and in-plane deformation response modes and also on the electric and magnetic potential. ACKNOWLEDGEMENTS The financial support of the Slovak Research and Development Agency under the contract No. APVV-18-0004 and VEGA 2/0061/20 are greatly acknowledged.