Hybrid carbon fibre-elastomer-metal laminates consist of alternating layers of carbon fibre reinforced plastics, elastomer layers and aluminium sheets. These laminates offer great potential for a lightweight structural material with adjustable damping properties. The material damping is strongly influenced by the viscoelastic properties of the elastomer layers which damp by the principle of constrained layer damping when the laminate is vibrated. In this study the material damping was experimentally characterised by three point bending dynamic mechanical analysis (DMA). In this regard, HyCEML specimens were tested on different frequencies and temperatures. The loss factor, storage-and loss modulus were measured to characterise the damping over the temperature and the frequency range. Time-temperature superposition was applied to determine the damping characteristics at higher and lower frequencies. The experimental results were compared to numerical studies on the basis of a characterisation of the single constituents. A test setup with a cantilever beam under free vibration was chosen for the comparison of experimental and numerical results. Detailed multi-layer finite element models were generated offering high flexibility in terms of type and number of finite elements especially in the direction of laminate thickness. For this purpose, existing material models were used to investigate the influence of each component on the system's damping behaviour. The damping in the free vibration experiments was determined with the logarithmic decrement at the free end. Also the numerically and experimentally determined first eigenfrequencies were compared. It could be shown that the laminate damping is strongly dependent on the glass transitions of both the carbon-fibre reinforced plastics and the elastomers. The numerically determined first eigenfrequency matched the experimental with a deviation of 10 %, the logarithmic decrement of the experimental results was more than 50 % higher. The damping behaviour of the HyCEM laminate, however, is underestimated by the numerical investigation, since nonlinear viscoelastic effects are not yet considered.