Abstract: In this paper, the stability of axisymmetric equilibrium modes of inhomogeneous circular plates with an elastically restrained edge, which are subjected to a normal pressure, is discussed. Assuming that the asymmetric component of the solution is periodic, the numerical method is used to determine the lowest load value, at which a bifurcation into the asymmetric state occurs. The influence of the degree of material inhomogeneity and the edge restraint conditions on the critical load and the buckling mode is investigated. It is shown that when the stiffness of the restraint that restricts the plate edge displacement increases in the radial direction, the asymmetric equilibrium modes can emerge under considerably higher loads and generate more waves in the circumferential direction. An increase in the elastic modulus of the plate toward its edge leads to an increase in the critical load, while the number of waves in the buckling mode does not change as compared to a homogeneous plate. When the elastic modulus decreases toward the plate edge the critical load decreases at weak constraints on the plate’s radial displacement.