When a composite material is subjected to a time-harmonic stress field (homogeneous or inhomogeneous), different phases undergo different temperature fluctuations due to the well-known thermoelastic effect. As a result irreversible heat conduction occurs within each phase and between phases, and entropy is produced. This entropy production is the genesis of elastothermodynamic damping and, as a consequence of the second law of thermodynamics, manifests itself as a conversion of work into heat. This paper is concerned with the calculation of elastothermodynamic damping in a matrix reinforced with hollow spheres. Numerical results are presented for an alumina/aluminum composite sphere subjected to a uniform radial stress at the outer boundary. When the cavity occupies more than 75 percent volume fraction of the alumina inclusion, the total damping becomes vanishingly small.