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Detailed knowledge of stress fields in critical regions of weldments is the necessary information for their strength and durability analysis. The stress information is subsequently used for finding where fatigue cracks may initiate and how fast they may grow. The method discussed below enables determination of stress concentration factors and stress distributions in weldments by using a special finite element modeling technique. It is known that detailed analysis of stress fields in weldments requires using very large number of very small finite elements. Therefore such an approach is in reality impractical. The proposed FE procedure requires using relatively Large Shell or Brick Finite Elements, comparable with the plate thickness, but the FE stress data is subsequently enriched by analytical extension. The procedure consists of a set of rules concerning the development of appropriate finite element models necessary to capture the hot spot bending and membrane structural stresses. The stress data obtained from the Shell or Brick Finite Element analysis and relevant analytical stress concentration factors are subsequently used to determine the peak stress and the nonlinear through thickness stress distribution. The peak stress at the weld toe can be subsequently used for estimating the fatigue crack initiation life. The stress distribution and the weight function method can be used for the determination of stress intensity factors and for the analysis of subsequent fatigue crack growth.