Nowadays, to reduce vibrations of machines, damping devices utilize the eddy current damping effect being increasingly investigated for its advantages of no mechanical contact, no viscous liquid required, high reliability, and good damping capacity. This article studied the main principle of the eddy current damping effect for a moving permanent magnet in a stationary and electrically conductive nonmagnetic cylindrical tube. The magnetic damping coefficient is investigated experimentally, analytically, and by numerical simulations in a steady-state. The numerical simulation is performed in the ANSYS Maxwell programme. The obtained results indicate that the damping force affecting the moving magnet has a viscous form. The experimentally measured and computed results are in good agreement. The effect of varying tube diameter and the tube wall thickness on the magnetic damping coefficient is shown. The contribution of this article consists in the development and a comparison of the obtained results of three approaches for determining the magnetic damping coefficient for a moving magnet in a cylindrical tube.