The different applications of micro/nano scale structures increase daily, and using new developed theories accounting
size-reduction effect can be useful to study mechanical behaviors of such structures. The size dependent
theory of modified strain gradient is capable for considering micro/nano structures. In the current work a new
model based on the modified strain gradient and three dimensional elasticity theories is developed for free
vibration of functionally graded (FG) micro/nano plates, and an exact analytical solution is carried out for
extracting the natural frequencies of it. The present three-dimensional elasticity model contains three length
scale parameters. Analytical solution is based on the state space method. In order to achieve the analytical
solution, the distribution of material properties through the plate thickness follows an exponential law. Finally,
some exact numerical results are tabulated for both homogeneous and FG plates that can be used as an exact
three dimensional elasticity benchmark for validate other two dimensional models.