A simple method named singularity length method (SLM) with a key parameter singularity length ‘as’ is proposed to estimate the shear stress distribution at the V-notch corner. For tube-flange welded joints (TFWJs) with 135° weld toe notches, the singularity length ‘as’ is observed to be determined by different geometries and is summarized into concise formulas. A rapid calculation method of the mode III notch stress intensity factor (NSIF K3) without any FEA process is presented based on the SLM. Good agreement is showed between the fine meshed FE, the coarse meshed FE for the strain energy density (SED) and the proposed method. Six fatigue tests data of TFWJs is collected to conduct fatigue strength assessments based on the nominal shear stress and the rapidly-calculated NSIF K3. The results shows the NSIF K3 can be well applied as a fatigue parameter.