In a classic paper, Clarence Zener  considered transverse vibrations of an isotropic, homogenous, thermoelastic beam. He observed that the tensile side of such a vibrating beam cools while the compressional side heats up, resulting in irreversible heat transfer. This observation led him to predict the existence of thermoelastic damping. Pas sive damping is a critically important property from the viewpoint of vibration suppres sion in large, flexible space structures. Unfortunately, Zener's model cannot be extended to calculate damping in heterogeneous materials; therefore, in this article a more funda mental approach is taken. The Second Law of Thermodynamics is taken as the starting point, and the thermoelastic damping is calculated from the entropy created by the irre versible heat transfer in the medium. As a first step toward constructing a general theory for thermoelastic damping in composite materials, we solve the problem of a three-layer beam subjected to uniaxial tension and pure flexure.