Abstarct: In this research, the mathematical solution of governing equations for vibrations of composite annular plates with auxetic core has been presented for different boundary conditions and the transverse loading. According the first order shear deformation theory and considering the Hamilton principle, the governing equations which are four couple partial differential equations are derived. The perturbation technique has been used for the modal analysis and response calculation. The quantities which have been considers are: determining the response in terms of the space and time, the natural frequencies, investigating the effect of the geometrical and mechanical parameters on the frequencies and response and comparing the results with the numerical solution. The results show that by increasing the thickness of the core laxyer, the transverse frequency increases but the radial frequency decreases.