This work describes a method of analyzing the vibration response of a viscoelastic beam. The equation of motion of the transverse vibration of a beam with viscous damping and temporal hysteresis is given. Several methods for measuring the constants of a given hysteresis kernel are presented. One is based on a least-squares fit to data using inverse procedures for partial differential equations. The second approach discussed is that of introducing an auxiliary coordinate. This coordinate combined with a transfer function model of the hysteresis effect yields a modal analysis solution for the viscoelastic beam. It is shown that identification is then possible by using modal analysis techniques. This theoretical derivation is compared with test data.