The internal friction of aluminium foams with various porosities was measured in the range of acoustic frequencies over a wide strain-amplitude range by the bending-vibration method. The measured internal friction shows that aluminium foams have a damping capacity which is enhanced in comparison with bulk aluminium, increases with increasing porosity, decreases with increasing frequency and increases with increasing strain amplitude. In order to explain the behaviour of the internal friction, a mechanism of internal dissipation energy was presented, and an approximate expression for internal friction is derived which is based on the equations of plane waves in elastic material with voids. This expression can account for the dependence of the internal friction on porosity, pore size and frequency. To gain further insight into the dependence of the internal friction on amplitude, the non-linear characteristics of oscillations were observed, and it was found that the resonance curves are asymmetric and the resonant frequencies are proportional to the square of amplitude with a negative slope. On the basis of the equations of the motion and the experimental results, the non-linearity of oscillations was ascribed to a non-linear damping term and an approximate expression for the damping coefficient with respect to amplitude was obtained.