A continuum approach is proposed to describe micro-inertia effects in closed-cell foams using a micromechanical method. An initially spherical unit-cell was considered and the influence of inertia at the unit-cell level was characterised with the use of a dynamic homogenisation technique. The contribution of micro-inertia appears in the form of a dynamic component of the macroscopic stress. A closed-form expression of the dynamic stress was obtained. The proposed modelling was applied to acoustic and shock wave propagation. In both cases, the influence of micro-inertia was found to be significant. The obtained results are in good agreement with existing data of the literature, provided by micromechanically accurate finite element computations and experiments. The proposed model is aimed to enhance continuum models of foam materials by taking into account the contribution of micro-inertia.