The fracture and fragmentation of concrete under static and dynamic loads are studied. The uniaxial compressive strength test is employed to study the concrete behavior under static loads while the split Hopkinson pressure bar is used to study the dynamic behavior of the concrete under static loads. The theories for acquiring the stress, strain and strain rate of the concrete in the dynamic test by Hopkinson pressure bar has been introduced. The fracture patterns of the concrete in the uniaxial compressive test have been obtained and the static concrete compressive strengths have been calculated. The fracture patterns of the concrete in the uniaxial compressive test have been obtained and the static concrete compressive strengths have been calculated. The fracture and fragmentation of the specimen under dynamic loads have been acquired and the stress-strain curves of concrete under various impact loads are obtained. The stress-strain curve indicates a typical brittle material failure process which includes existing micro-fracture closure stage, linear-elastic stage, nonlinear-elastic stage, and post-failure stages. The influence of the loading rate for the compressive strength of the concrete has compared. Compared with the concrete under static loads, the dynamic loads can produce more fractures and fragments. The concrete strength is influenced by the strain rate and the strength increases almost linearly with the increase of the strain rate.