The damping behaviour of continuous carbon fibre and flax fibre reinforced polymer (CFRP and FFRP) composites was studied by comparing angle-ply laminates. Using logarithmic decrement measurements, dynamic mechanical analysis and vibration beam measurements, the damping was described as the specific damping capacity ψ in order to compare data using the different methods. Our results show approximately 2–3 times better damping of FFRP compared to CFRP at low frequency and low strain. We show that the damping of both materials increases with increasing angle-ply orientation below 300Hz. While the matrix and interface seems to contribute mainly to damping at lower frequencies, the fibre shows an increasing contribution with ψ = 64.4% for unidirectional FFRP at 1259Hz in the 5th mode of vibration, without a notable change in the elastic modulus. This work demonstrates that the FFRP may be simultaneously stiff and efficient at damping.