Nonaxisymmetrical buckling of inhomogeneous annular plates subjected to normal pressure is studied. The effect of material heterogeneity and ratio of inner to outer radii on the buckling load is examined. The unsymmetric part of the solution is sought in terms of multiples of the harmonics of the angular coordinate. A numerical method is employed to obtain the lowest load value, which leads to the appearance of waves in the circumferential direction. For an annular plate with a small inner radius of a plate and Young’s modulus, decreasing towards the outer edge, the critical pressure for unsymmetrical buckling is sufficiently lower than for a plate with constant mechanical properties. For an annulus with large inner radius, the buckling pressure and the buckling mode number increases as the Young modulus decreases towards to outer edge of a plate.