Rayleigh-Taylor instability of three fluid layers with two interfaces in cylindrical geometry is investigated analytically.The growth rates and the amplitudes of perturbation on the two interfaces are obtained.The feedback factor from outer to inner interface is larger than that from inner to outer interface under the same conditions.The growth rate on the initially unstable interface is larger than the corresponding result in planar geometry for low mode perturbation.The two interfaces are decoupled for a larger mode number perturbation.The dependencies of the amplitudes of perturbation on different initial conditions are analyzed.The negative feedback effect from initially stable interface to another unstable interface is observed.In the limit of infinity inner radius and finite shell thickness,the results in planar geometry are recovered.