In the present paper, for the first time, theoretical analysis for static, dynamic, and transient responses of micro-plates made of different materials were comprehensively performed. The constitutive relations of analyzed materials satisfy assumptions of the modified couple stress theory. Additionally, values of length scale parameters of studied materials are taken from well-established experimental results presented in the literature. A generalized model of micro-plates made from Cu, Ni, Ti, and Epoxy satisfies assumptions of Reissner–Mindlin plate theory. The formulated generalized boundary value problem is solved by analytical and the radial basis function finite difference (RBF-FD) methods. A convergence study is performed to show the advantages and correctness of the obtained numerical solution. The meshless numerical method is easy to implement and it provides accurate results that are in excellent agreement with analytical solutions. Effects of material parameters, boundary conditions, and assumptions of classical and the modified couple stress theory on the static bending, free vibration and transient responses of micro-plates are presented and discussed.