Abstarct: The aim of this work is studying the vibration of an elastic, thick, finite and hollow cylinder when subjected to the constant angular velocity that the Flywheel of the satellite electromechanical battery is one of its applications. This goal is investigated on the basis of the linear 3D theory of elasticity and an analytical solution is presented. At first a general solution for the vibration of the cylinders affected by the general body force is offered. For this purpose the Navier equation in cylindrical coordinates expressed. The reason of using Navier equation is getting accurate solution, less calculations and executable for different geometries and different materials. With using the orthogonalization technique more boundary conditions are satisfied. Then with using the relations between displacement and force and also the equation of tensions the matrix of the equations can write. Some of boundary conditions are approximately satisfied using orthogonal property of the Trigonometric and Bessel functions. Then the frequencies are extracted. The vibration of the cogging torque does produces in Flywheel of the electromechnical battery because of the interactive between magnet poles and machine slot that doesn’t do that studied with presented method. In this dissertation for deriving the numerical results using Maple code. The numerical results are compared with the last researches for static cylinders.