Abstract This paper proposes penalty factor equations that take into consideration the weld strength over-match given in the classified form similar to the revised equations presented in the Code Case N-779 via cyclic elastic-plastic finite element analysis. It was found that the K e analysis data reflecting elastic follow-up can be consolidated by normalizing the primary-plus-secondary stress intensity ranges excluding the nonlinear thermal stress intensity component, S n to over-match degree of yield strength, M F . For the effect of over-match on K n × Κ ν , dispersion of the K n × Κ ν analysis data can be sharply reduced by dividing total stress intensity range, excluding local thermal stresses, S p-lt by M F . Finally, the proposed equations were applied to the weld between the safe end and the piping of a pressurizer surge nozzle in pressurized water reactors in order to calculate a cumulative usage factor. The cumulative usage factor was then compared with those derived by the previous K e factor equations. The result shows that application of the proposed equations can significantly reduce conservatism of fatigue assessment using the previous K e factor equations.