The main concern of this paper is the modelling of material damping in composite structures. A method is derived to predict the homogenized damping properties analytically. The procedure is based on the micromechanical theory of a representative fibre-matrix cell. Since the dissipative phenomena cannot generally be defined by a unique mathematical model, an equivalent viscous damping model is suggested. On the structural level damping can be analysed by the finite element method. Modal damping is illustrated by numerical applications.