Fatigue design rules for welds in the ASME Boiler and Pressure Vessels Code are based on the use of Fatigue Strength Reduction Factors(FSRF) against a code specified fatigue design curve generated from smooth base metal specimens without the presence of welds. Similarly, stress intensification factors that are used in the ASME B3l.1 Piping Code are based on component S-N curves with a reference fatigue strength based on straight pipe girth welds. But the determination of either the FSRF or stress intensification factor 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. In this paper, a mesh-insensitive structural stress method is used to re-evaluate the S-N test data, and then more effective method is proposed for pressure vessel and piping fatigue design.