The composite material shafts have been sought as new potential candidates for replacement of the conventional metallic shafts in many applications. These shafts are proved to have not only lighter in weight but also have greater strength. However, detailed dynamic studies on the effects of different materials, speeds and unbalance response are required, particularly with respect to the damping present due to the composite material. The main aim of the paper is to estimate the damping in rotor system consists of a composite solid shaft. The study is carried out to analyze the dynamic behaviour at different speeds and for different materials such as glass/epoxy, carbon/epoxy. Three different methodologies have been carried out for determining the damping of the composite shaft- rotor. The first one is to measure the signal at any speed, with impact hammer and get the logarithmic decay curve at that speed. From this the damping was estimated. The second method is to use half-power method to estimate the damping from the response of the rotor. In third methodology force sensors are used to get the unbalance force of the system and consequently hysteresis loops are obtained between the force and displacement for different speeds to get the equivalent damping. Simultaneously the Finite Element Analysis of the same rotor system using ANSYS software is carried out for eigenfrequencies. These results for different materials are compared with those of experiments.