Abstract In this paper, the free axisymmetric vibrations of circular sandwich plates with relatively stiff core of parabolically varying thickness have been presented on the basis of first order shear deformation theory. For the present model, the plate is assumed to be symmetric with respect to the middle surface. The facings are taken of the same material and of the same thickness. Due to parabolic variation in thickness of the core, facings take the shape of paraboloid of revolution and membrane forces of facings contribute to the transverse shear and bending of the core of sandwich plate. The equations of motion have been derived by Hamilton's energy principle. The first three natural frequencies for clamped, simply supported and free edge conditions have been obtained using a differential quadrature method, taking the grid points as zeros of Chebyshev polynomials. The effect of various plate parameters such as taper parameter, facing thickness and core thickness on the frequency parameter has been investigated. Comparison of results for some special cases with published results obtained from other approximate methods has been presented which shows an excellent agreement. Mode shapes for specified plates have been plotted. © 2015 Elsevier Ltd.