Flexural vibration in a homogeneous isotropic heat conducting cylindrical panel resting on the elastic medium (Winkler model) is investigated in the context of Coupled theory of thermoelasticity (CT) and Lord-Shulman (LS) generalized theory of thermoelasticity. The analysis is carried out by introducing three displacement potential functions so that the equations of motion are uncoupled and simplified. A modified Bessel function solution with complex arguments is then directly used for the case of complex eigen values. In order to illustrate theoretical development, numerical solutions are obtained for non-dimensional frequency, attenuation coefficient (symmetric and skew symmetric) and are presented graphically for a zinc material. The numerical results indicate that the effect of thermal relaxation time and the damping of embedded medium on the non-dimensional frequency are very pronounced and also LS model is suitable for elastic material.