Fatigue verification of Class 1 nuclear power piping according to ASME Boiler and Pressure Vessel Code, Section III, NB-3600, which is often discussed in connection to power uprate and life-extension of aging reactors in recent years, is dealt with. Key parameters involved in the fatigue verification, e.g., the alternating stress intensity S alt , the penalty factor K e and the cumulative damage factor U, and relevant computational procedures applicable for the assessment of low-cycle fatigue failure using strain-controlled data, are particularly addressed. A so-called simplified elastic-plastic discontinuity analysis for alternative verification when fatigue requirements found unsatisfactory, and the procedures provided in NB-3600 for evaluating the alternating stress intensity S alt, are reviewed in detail. An in-depth discussion is given to alternative procedures suggested earlier by the authors using nonlinear finite element analyses, which uses a nonlinear finite element analysis for directly determining the alternating stress, thus eliminating uncertainties resulted from the use of the penalty factor K e . Using this alternative, unavoidable plastic strains can be correctly taken into account in a computationally affordable way, and the reliability of the verification will not be affected by uncertainties introduced in the simplified elastic-plastic analysis.