Summary: The thermoelastic damping due to thermal currents and the electromagnetic damping due to electric conduction currents of vibrating solids are discussed. The effects of structural and geometrical constraints on damping loss factors are investigated. Also, optimum conditions for the maximum damping, which may be useful on the stage of system design, are investigated. It is found that damping loss factors are generally dependent upon structural and geometrical configurations. An analogy exists between thermoelastic damping and electromagnetic damping, showing Debye curves with Debye peaks. Standing transverse waves are likely to achieve larger damping than standing dilatational waves in the presence of a magnetic field. Electromagnetic damping in ferromagnetic material bodies is found to be considerable in high field. The influence of thermoelastic damping on aeroelastic stability of beam plates is investigated. This research strongly suggests that thermoelastic damping improves the aeroelastic stability of beam plates.