This paper presents the free vibration analysis of a circular plate with a concentric square hole. The boundary condition is the edge of the square hole is free and the outer circular plate is simply supported. Due to the geometric abnormality, this analysis does not permit an exact solution. The present problem deals with the numerical calculation of the natural frequencies and mode shapes of vibration of the structure by independent coordinate coupling method(ICCM). The numerical results show the efficacy of the ICCM and changes in natural frequencies and modes due to the square hole size.