Mechanical energy loss, in automobile tires, as well as other products made of cord reinforced rubber composites, is a major source of energy-consumption. To minimize the energy loss, it is essential to increase the understanding of the way in which internal losses in a composite depend on the loss characteristics of the constituents used to fabricate it. In this paper, the application of the viscoelasticity theory in predicting the loss characteristics is discussed in detail. The scope and the limitations of the linear theory, the relations between the effective loss characteristics and constituents’ properties, and the numerical methods for predicting the loss moduli are discussed. Some numerical results are presented .