Based on the Reissner assumptions, the free vibration analysis of simply supported cylindrical and rectangular sandwich panels with isotropic face sheets and a functionally graded core is concerned. Firstly, the expressions of the displacements, stresses and internal forces are presented according to the constitutive relations and stress states of the core and face sheets. Then, the dynamic stability and compatibility equations are given for cylindrical sandwich panels with functionally graded core, elastic modulus and density in which vary continuously in the thickness direction. Finally, the proposed solutions are validated by comparing the results of degenerate example with classical solutions, and a numerical analysis is performed on the example of simply supported cylindrical and rectangular sandwich panels. The elastic modulus and density of the functionally graded core are assumed to be graded by a power law distribution of volume fractions of the constituents, and the Poisson ratio is held constant. The effects of the distribution of functionally graded core's properties, the thickness-side ratios and ratio of radius $(R)$ to length $(l)$ $\kappa =R/l$ are also examined.