Study on the dynamic behavior of concrete is important, for the sake of seismic design and safety evaluation of mass concrete structures, such as concrete dams, nuclear reactors and so on. There have been a lot of uniaxial strength experiment data of concrete under dynamic loading, but multiaxial data is scarce, for the test of multiaxial strength of concrete under dynamic loading is difficult, while most mass structures work under multiaxial static and dynamic stress states. In this paper a three-dimension failure criterion of concrete under dynamic loading in octahedral stress space was proposed. Then the multixial strength tests of concrete under dynamic loading were carried out with concrete triaxial static and dynamic apparatus system. The selected loading paths consisted of uniaxial compression and tension, biaxial proportional loading compression, biaxial compression with one constant lateral compression and triaxial compression with two constant lateral compressions. In the test the strain rate range is 10-5~10-2/s. Based on the test data and the literature data, the characteristic of this failure surface is that it considered the influence of the strain rate and the angle of similarity; it is smooth, convex in meridian and deviatoric plane. The proposed model for nonlinear dynamic analysis and design of mass concrete structures under dynamic loading is useful.