An analytical method is presented for predicting the effect of a local deviation in the form of a concentrated mass along a radial line on the free bending vibration characteristics of a nearly axisymmetric circular plate. The approach is based on the Rayleigh-Ritz method and the expression of local deviation of the concentrated radial mass as the variation of heaviside unit step function. The effects of the concentrated mass on the natural frequencies and mode shapes of the plate are predicted with a proposed nondimensional mass parameter.