Strengths of large aggregate concretes and the corresponding wet screened concretes were studied experimentally. Specimens were subjected to dynamic triaxial compression compression tension stress, using large concrete static and dynamic triaxial servo test system. Results show that failures of the two kinds of concretes are typical tensile failures, and the cracks are perpendicular to the tensile stress direction. Their dynamic tensile strength increases with the increase of strain rate, and decreases with the increase of compressive stress. The increasing coefficient of tensile strength and the logarithm of strain rate ratio are in linear relationship. Dynamic tensile strength and its sensitivity to strain rate of large aggregate concretes are lower than those of the wet screened concretes. By fitting the experimental data, failure criteria in octahedral stress space were established, which provides an experimental basis for nonlinear analysis and seismic design of mass concrete structure.