The damage rule of concrete is theoretically analyzed and discussed from the aspects of the stiffness degradation and the cohesive strength degradation. Further, the multiaxial damage rules of concrete are studied by 25 groups of tests under true triaxial and conventional triaxial compressive cyclic conditions. The analysis of the test results shows that the relationship between the damage variable and the axial plastic strain depends on the loading path. This dependence of the damage variable on the stress paths can be normalized by the equivalent plastic shear strain. A partial differential equation of the damage variable, driven by the equivalent plastic shear strain, is constructed based on two characteristic boundary conditions of the damage gradient. Then, a stress-path-independent isotropic damage variable is proposed by the integral of the partial differential equation. The proposed damage variable can reasonably capture the multiaxial damage behavior of the concrete. The stress path independence of the proposed damage variable is analyzed and further verified by the test results under multiaxial stress conditions.