Abstract: The generalized differential quadrature method(GDQM)developed recently is more and more widely used in structural analysis,but it is restricted by some conditions.The finite element method(FEM)is a conventional numerical method,but the computational effort is significant.In this paper,GDQM and FEM are combined together to analyze the transverse vibration of circular plates with an elastically mounted mass.This combination first proposed in this paper is a new way to solve the problems with complex domains in structural analysis.It is a rapid,efficient,accurate and flexible numerical method with both the advantages of GDQM and FEM.Comparison with the existing literature has proved that the results obtained by this method are very accurate.