High‐efficiency algorithms are proposed for numerically integrating elasto‐plastic rate equations for the purpose of simulating metal failure effects under repeated loading conditions. Results are obtained with a newly established elasto‐plasticity model which can automatically simulate both low and high cycle fatigue failure effects, with reference to neither damage‐like variables nor ad hoc failure criteria. Novelties are incorporated in a few respects. First, multiaxial loading processes with arbitrarily changing principal stresses and axes can be treated in a broad sense beyond usually treated proportional loading cases. Second, by means of the commonly used J2‐invariant of the deviatoric stress, multiaxial loading cases can be directly treated just as in the uniaxial loading case. Third, high cost in time consumption can be considerably reduced in evaluating both low and high cycle failure effects. Numerical examples are presented for simulating uniaxial and multiaxial fatigue failure effects and simulation results are in good agreement with experimental data. Results show that the computation speed with the new algorithms exceeds 600 times faster than usual integration algorithms.