In this study, free axisymmetric vibrations of composite circular sandwich plates with isotropic core and orthotropic facings have been studied using first-order shear deformation theory. The thickness of the core is assumed to vary exponentially in the radial direction and the face sheets is treated as membrane of constant thickness. The effect of shear deformation and rotatory inertia in the core has been taken into account. The governing differential equations of the present model have been obtained by applying Hamilton's principle. Chebyshev collocation technique has been used to obtain the frequency equations for the plate when it is clamped or simply supported or free at the edge. The first three roots of these equations have been reported as the natural frequencies for the first three modes of vibration. The effect of 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 by other approximate methods has been presented which shows an excellent agreement. Mode shapes for a specified plate for all the three boundary conditions have been plotted. © 2019 Elsevier Ltd