In the present paper, axisymmetric vibrations of a circular sandwich plate with relatively stiff core of exponentially varying thickness have been investigated. The face sheets are treated as membranes of constant thickness and the core is assumed to be solid as well as moderately thick. The equations of motion have been derived using Hamilton’s energy principle. The frequency equation for clamped boundary condition is obtained by employing harmonic differential quadrature method. The lowest three roots of this equation have been reported as the frequencies for the first three modes of vibration. The effect of various plate parameters on the natural frequencies has been studied. Three-dimensional mode shapes for a specified sandwich plate have been illustrated. A comparison of the results with published work has been made. © Springer India 2015.