Extensive measurements of the internal friction in a variety of layered materials such as graphite, metal dichalcogenides (MoS2, TiS2, NbSe2, TaS2, TaSe2, and TaTe2), and montmorillonite clays are reported. The internal friction of these layered materials exhibits features similar to those observed in graphite. In particular, a high temperature internal friction plateau develops at a temperature that is characteristic of the material. The physical mechanism for this plateau is discussed.