In order to calculate the multi-axial strength of concrete and design a concrete structure considering the multi-axial strength of concrete, a general method for calculating the multi-axial strength under an arbitrary multi-parameter strength criteria is presented in this paper by using the overload factor of equivalent ratio, K_OL. Taking a completed arch dam as an example, the equal proportional overload factor, K_OL, and the failure distance factor, K_FD, are calculated, respectively, and compared with the safety factor of uniaxial strength. Then, the necessity of designing a concrete arch dam according to the multi-axial strength is pointed out. Based on the definition of K_FD and the analysis of an example, it is suggested that K_FD should be consideredas an index for the safety design and the checking of multi-axial strength of arch dams.