The damping of perfectly bonded CFRPs may only be increased by increasing the energy dissipation in the matrix. Accordingly the use of short fibres results in a slight increase in loss factor for a negligible sacrifice in stiffness by introducing shear strain magnification at the fibre tips. However, selection of a highly dissipative matrix resin along with the careful design of fibre lay-up yielded a stiff light CFRP with substantially increased damping. An experimental apparatus was designed and built, which enabled the loss factors of CFRPs undergoing both applied and induced combined shear and flexural vibrations to be measured. Predictions of combined mode damping behaviour were made according to existing equivalent strain analyses applied firstly to the CFRP as a macroscopically homogeneous material and secondly to the resin as the dissipating phase of the CFRP. The former produced qualitative agreement with experimental results, although physical considerations suggest this agreement to be coincidental only. The latter analysis was concluded to be more representative although the effects of shear deformation ignored in the model were found to be highly significant. Examination of the effects of high dynamic strain amplitudes on the structural damping of longitudinally restrained members necessitated a revision of the fundamental definition of structural loss factor and the implications of linear material damping. Consequently the basic assumption that for a linearly damped material structural loss factor equals the material loss factor was contradicted. High amplitude strains were found to have negligible effect on resin or CFRP damping, whilst induced axial strains significantly reduced the flexural loss factor. Experimental results endorsed the theoretical models. CFRPs, like resins, displayed essentially linear damping characteristics throughout the investigations. Future analyses of damping should concentrate on energy dissipation in specimens rather than their loss factors.