In this paper, a general approach is proposed for modeling the behavior of concrete under biaxial fatigue loading with various mean stresses (stress range). Using damage mechanics and principles of thermodynamics, a generalized bounding surface approach is proposed. It is mentioned that limit surface, determined by model, is a condition in which the number of fatigue loading is set to one. In other words, limit surface represents the strength of material under monotonic loading with various load paths. By increasing the number of loading cycles, the limit surface is allowed to contract and to form surfaces representing residual strength curves. The evolution of the subsequent surfaces depends on load magnitude, load range (mean stress), and load path. Within the formulation, a softening function is postulated which captures the reduction in the strength of concrete under fatigue loading. A comparison of model predictions against experimental data shows a good correlation.