The notch stress approach for fatigue assessment of welded joints is based on the highest elastic stress at the weld toe or root. In order to avoid arbitrary or infinite stress results, a rounded shape with a reference radius instead of the actual sharp toe or root is usually assumed. IIW recommendations for the fatigue assessment of welded structures by notch stress analysis reviews different proposals for reference radii together with associated S-N curves. Detailed recommendations are given for the numerical analysis of notch stress by the finite or boundary element method. Several aspects are discussed, such as the structural weakening by keyhole-shaped notches and the consideration of multiaxial stress states. Appropriate S-N curves are presented for the assessment of the fatigue strength of different materials. Finally, four examples illustrate the application of the approach as well as the variety of structures which can be analysed and the range of results that can be obtained from different models.