The magnetic rubber damper with a constraining layer (MRDC), which we developed, is easy to install on steel vibrating objects and has proven to be an excellent vibration damper. The damping property of an MRDC is substantially attributable to the frictional loss between its magnetic rubber layer and a steel object. The authors devised a theory to predict its damping properties by taking friction into consideration, the theory itself being based on an analysis of the flexural vibration of a beam with MRDC. The accuracy of the proposed theory has been verified by comparing analytical and experimental results, and a design to optimize MRDCs has been determined from those obtained from calculation and measurement.