Strain-rate effects on the behaviour and on failure of concrete under quasi-static and dynamic loading (with uniaxial strain-rates up to 1000 s−1) are investigated from both experimental testing and modelling point of views. The main damaging process taken into account is the brittle tensile response induced by Poissons' effects under compression loading. The proposed meso-mechanical model is based on a description of mechanisms observed at a microscopic level after failure has started. The strain-rate sensitivity then appears as a consequence of the motions of such mechanisms, with the introduction of the time derivative of the strain-rate (ϵ̈) in the formulation. Dynamic loadings under compression are performed with a Split Hopkinson pressure bar (SHBP) apparatus. To investigate the response of concrete under multiaxial loading, a specific device presented in the paper is specially built to produce dynamic compression under various controlled lateral confinement pressures, allowing for an independent evaluation of radial inertia and lateral pressure effects. It is found that a small number of parameters, mostly deduced from a classical pure compression or traction test, allow for correct modelling of the response under multiaxial loading for a wide range of speeds of loading.