Triaxial stress states have a considerable effect on the material strength of concrete in case of both, monotonically increasing as well as cyclic loads. Based on two suitable multiaxial strength models mechanical models for the fatigue failure of normal strength concrete respectively high-performance and ultra-high-performance concrete are developed. The five parameter model by WILLAM/WARNKE is used for normal strength concrete. Two energy based damage variables were introduced into the model, which allow the mathematical description of damage from cyclic loading. Using this model in numerical simulations of structures the evolution of strains and the damage-depending redistribution of stresses can be displayed realistically. For the description of the fatigue failure of high-performance and ultra-high-performance concrete, the three-phases model by GRÜNBERG is more appropriate than the five-parameter model. Several areas of the model were calibrated using triaxial laboratory tests. To fully validate the model, further tests are required, especially in the range of high numbers of load cycles.