Based on the base force element method (BFEM), the dynamic mechanical behavior of concrete under uniaxial compression loading at different strain rates is investigated. The concrete can be considered as a three-phase composite material composed of aggregate, cement mortar, and interfacial transition zone (ITZ) on the meso-level. A two-dimensional random aggregate model is generated by the Monte Carlo method. A multi-linear two-dimensional damage model is applied to describe the damage properties of each phase in the concrete. The strain-softening behavior, strain-rate effect, and failure patterns of the concrete are studied. The numerical results find that the peaks of compressive stress and compressive strain of concrete show the rate-sensitivity in various degrees under different strain rates. The calculated results of the dynamic enhancement factors are in a good agreement with the formula given by the Comité Euro-International du Béton (CEB) and other experimental results. The failure diagram of the specimen clearly describes the compressive failure process of the concrete specimen. This failure`s characteristics are similar to the experimental results.