In the present paper, analysis and numerical results are presented for free axisymmetric vibrations of circular sandwich plate with isotropic core and polar orthotropic face sheets employing harmonic differential quadrature (HDQ) method. The thickness of the core is assumed to vary quadratically in the radial direction and the face sheets are treated as membranes of constant thickness. The effect of shear deformation and rotatory inertia in the core has been taken into account and the mathematical analysis is based upon Mindlin’s theory/first-order shear deformation theory. The governing differential equations of motion of the model have been obtained by using Hamilton’s energy principle. In the resulting equation HDQ method is employed to obtain the frequency equations for the three edges, namely; clamped, simply supported and free. The lowest three roots of these equations have been reported as the frequencies for the first three modes of vibration for all the three plates. The effect of various plate parameters such as taper parameter, core thickness at the centre and facing thickness on the natural frequencies has been studied. Three-dimensional mode shapes for the specified plates have been illustrated. To check the validity of the present considerations and the technique, frequency parameter has been compared in particular cases. © 2015, Springer Science+Business Media Dordrecht.