The continuous and gradual changes in material properties in one or more dimensions lead to exposure unique features. The Functionally graded materials (FGM) are one of these materials formed by two metal and nonmetal phases. Reduction in stress concentration, improving its distribution and better control of thermal stresses are portion of the FGM materials advantages. In resent years FGM beams and plates in micro and nano scales are considered as an essential parts in making the microelectromechanical, nanoelectro mechanical, atomic force microscope and other structures of such scales. Lack of conformity on laboratory tests results and normal; TEXT-INDENT: 14.4pt; MARGIN: 0cm 0cm 0pt; mso-pagination: widow-orphan; mso-layout-grid-align: none" Higher order deformation theories can be normal; TEXT-INDENT: 14.4pt; MARGIN: 0cm 0cm 0pt; mso-pagination: widow-orphan; mso-layout-grid-align: none" In this dissertation, based on the modified strain gradient and couple stress theories, stability of FGM plates subjected to mechanical (uniaxial, biaxial and shear load) and thermal (with uniform, linear and nonlinear temperature change) loading and free vibration are studied. The normal; TEXT-INDENT: 14.4pt; MARGIN: 0cm 0cm 0pt; mso-pagination: widow-orphan; mso-layout-grid-align: none" Key words : FGM microplates, modified strain gradient theory, modified couple stress theory, buckling, free vibration, finite strip method.