In this paper cyclic quasi-static and constant amplitude fatigue responses of concrete subjected tensile compression-tension (C-T) biaxial stress are presented. In the tensile C-T region within the biaxial stress space, magnitude of the principal tensile stress is larger than or equal to that of the principal compressive stress. An experimental program consisted of subjecting hollow, cylindrical concrete specimens to torsional loading. Failure in both quasi-static and fatigue is due to crack propagation. It is shown that the crack propagation resulting from the biaxial loading can be predicted using Mode I fracture parameters. The fatigue crack growth is observed to be a two-phase process: an acceleration stage that follows a deceleration stage. The crack length where the rate of crack growth changes from deceleration to acceleration is shown to be equal to the crack length at the quasi-static peak load. Analytical expressions for crack growth in the deceleration and acceleration stages are developed in terms of the mechanisms that influence quasi-static crack growth. The model parameters obtained from uniaxial fatigue tests are shown to be sufficient for predicting the biaxial fatigue response. Finally, a fracture-based fatigue-failure criterion is proposed, wherein the fatigue failure can be predicted using the critical Mode I stress intensity factor.