In this paper axisymmetric vibration of circular sandwich plates with honeycomb core of linearly varying thickness has been studied. The facings are of the same thickness and of the same material, are treated as membranes. The facings take the shape of conical shell due to linear thickness variation in the core and hence membranes forces of the facings contribute to the transverse shear of the core. The equations of motion for such a plate have been derived by Hamilton’s energy principle. The frequency equations have been obtained by employing differential quadrature method for three different boundary conditions at the edge, namely, clamped, simply supported and free. The lowest three roots of these frequency equations have been obtained for various values of different plate parameters and reported as the frequencies for the first three modes of vibration. Three dimensional mode shapes for specified plates have been presented. Comparison of results with published work has been made. © Springer India 2014.