The paper is concerned with modelling the dynamic behaviour of a structure with damping. Hysteretic damping is commonly accepted to be reasonably accurate in some circumstances, but can only be applied directly in the frequency domain. Dynamic (time) behaviour, however, is most conveniently predicted by a viscous model. A damping matrix is constructed for use in the viscous equation which gives a dissipation of energy approximating to the hysteretic model. The approximation is justified by comparing results in the frequency and time domains and against measured data from a loudspeaker diaphragm. The ability of the matrix to reflect different damping in various components of the structure is considered, together with predicted natural frequencies and modes.