Asymmetrical buckling of pressurized nonuniform shallow shells with elastically restrained edge under normal pressure is studied. The load is applied internally to the shell. 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 at which waves in the circumferential direction can appear. The effect of material heterogeneity and boundary on the buckling load is examined. If the outer edge can move freely in the radial direction, decreasing of the elasticity modulus to the shell (plate) edge leads to sufficient lowering of the buckling pressure. For a shell with ellastically restrained edge, the buckling pressure and mode number increase with a rise of spring stiffness.