This paper proposed a method to calculate the nature frequencies of generally supported plate with hole. The boundary of plate is considered as the combination of rotational springs and translational springs. The generally characteristic equations of generally supported plate with damage can be derived using Rayleigh-Ritz method. The nature frequencies of damaged plate can be obtained by solving the generally characteristic equations. The calculated results by proposed method were compared with that of FEM (finite element method) and analytical solutions. The compared results demonstrated that the proposed method is accurate and effective. Numerical examples are presented to analyze the effect of damage on the plate under different kinds of elastic restraint. The results suggest that: the effect of damage is little to the first order nature frequency and is relative large to the third order nature frequency when the rotational restraints are weak; the effect on the first order nature frequency rises but the effect on the third order nature frequency fall as the rotational restraints increase.