Concrete might be subjected to impact or blast loading. To analyze the concrete behaviors under such loading cases, it is of interest to study the dynamic damage and failure behavior of concrete under high strain rate. In the present paper, a mesoscale model is developed to numerically analyze the dynamic damage process of concrete samples under high strain rate tension. In the mesoscale model, the concrete is regarded as a three-phase composite consisting of coarse aggregate, mortar matrix, and interfacial transition zone (ITZ) between the aggregate and the mortar matrix. Different coarse aggregate shapes, such as circular, oval, and polygon, are calculated and compared. It is found that the shapes of the coarse aggregates do affect the tensile strength and failure pattern.