This chapter develops the Reddy third-order shear deformation plate theory (TST) of the axisymmetric circular plates. It argues that both the classical and first-order plate theories are fourth-order theories whereas the Reddy third-order plate theory is a sixth-order theory. The order referred to here is the total order of all equations of equilibrium expressed in terms of the generalized displacements. The Reddy of axisymmetric circular plates, which is an extension of the Reddy third-order beam theory, is developed accounting for material variation through the thickness, the von Karman nonlinearity, and the effect of the modified couple stress. The chapter presents exact solutions (by direct integration) of the theory for the linear case and bending relationships between the classical and third-order plate theories.