The present work deals with the free axisymmetric vibrations of circular sandwich plates with core of linearly varying thickness. The face sheets are treated as membranes of equal thickness and the core is assumed to be solid as well as moderately thick. The plate is assumed to be symmetric about the middle surface. Due to linear thickness variation in the core, the face sheets take the shape of conical shell and because of this the face sheet membrane forces contribute to the bending and transverse shear of the core of sandwich plate. The effect of transverse shear and rotatory inertia has been retained in the core. The equations of motion for such a plate have been derived by Hamilton's energy principle. The frequency equations for three different boundary conditions have been obtained by employing differential quadrature method. The effect of various plate parameters such as taper parameter, thickness of the core at the center, face thickness on the natural frequencies has been studied. Comparison of results has been made. © The Author(s) 2014.