Viscoelastic damping materials with a constraining layer have excellent damping properties, but they have a weighty drawback that many works, such as preliminary treatment of adhesive surfaces and hold of viscoelastic damping materials till adhesive is completely stiffened, are required. To overcome this drawback, magnetic rubber dampers with a constraining layer (MRDC), which are composed of two layers-a magnetic rubber layer and a constraining steel layer-have been developed. They are easy to be fixed onto steel objects due to the attractive force of magnetic rubber layer. The damping property of MRDC is substantially caused by the friction loss which arises between the magnetic rubber layer and the steel object. The equation of loss factor of a beam with a sheet of MRDC is derived by taking the friction loss into account to analyze the flexural vibration of the beam.