Free vibration of three layered sandwich cylinders is considered.The flexural vibration of the main elastic cylinder is damped using viscoelastic core which is discontinuously constrained by number of elastic segments around the circumference.The core layer is assumed to be linear viscoelastic with complex elastic moduli.In development of analytical procedure the governing equation for the free vibration of damped system is formulated.As a result a sixth order differential equation for the motion is derived.This equation has the same form as that reported by Mead and Markus for a continuously constrained three layer sandwich beam.Six boundary conditions in terms of flexural displacement are satisfied for fixed-free and free-free discontinuously damped sandwich cylinders.The determinant of coefficient matrix is then equated to zero and roots are computed using iteration method.A parameter study is conducted and dimensionless frequencies and the loss factors are computed for different shear parameter,geometric parameter,and the core loss factor.The ranges of these parameters are sufficient to cover most cases which are encountered in practice for the first three modes of vibration.