The stabilization of the ratio of P to S energy in the multiple scattering regime was first predicted theoretically by Weaver (1982) and has been recently observed in the high-frequency coda of earthquakes by Shapiro et al. (2000). The goal of this note is to extend previous theoretical results to the case where anelasticity is present in the medium. Our study demonstrates that even if there is preferential absorption of one of the modes (P or S), a stabilization occurs in the multiple scattering regime. The new equilibrium ratio is shifted in favor of the mode that is least absorbed but rarely differs by more than 15% from the ratio predicted for purely elastic media.