Fatigue design rules for welds in the ASME Boiler and Pressure Vessel Code are based on the use of Fatigue Strength Reduction Factors (FSRF) and a Code-specified fatigue design curve generated from smooth base metal specimens without the presence of welds. Similarly, Stress Intensification Factors (SIF) that are used in the ASME B31 Piping Codes are based on component S-N curves with a reference fatigue strength based on straight pipe girth welds conducted by Markl et al in 1950s. Typically, the determination of either the FSRF or SIF requires extensive fatigue testing to take into account the stress concentration effects associated with various types of component geometry, weld configuration, and loading conditions. As the fatigue behavior of welded joints is being better understood, it has been generally accepted that the difference in fatigue lives from one type of weld to another is dominated by the difference in stress concentration. However, general finite element procedures are currently not available for effective determination of such stress concentration effects. This is mainly due to the fact the stress solutions at a notch (e.g. at weld toe) are strongly influenced by mesh size and element type at and near a weld, which are a result of the notch stress singularity.