General expressions are derived for the loss factors of axially uniform linear composite structures in terms of properties of the constituents. Specializations applicable to practical composites incorporating free and constrained viscoelastic components are introduced. The results are shown to be generalizations of earlier studies of coated and sandwich plates [Ross, Ungar, Kerwin, Sec. 3 ofStructural Damping, ASME (1959)], and it is demonstrated that much of the abundant information available for such plates may be carried over to more complicated structures by redefinition of the structural and shear parameters.