To account for the effect of the stress concentration factor (SCF) at the weld toe on stress intensity factor range ΔK, a magnification factor Mk is used. The existing Mk solutions given in BS 7910 were developed for the fatigue assessment of flaws at the toes of fillet and butt welds and may not be suitable for assessing flaws at single-sided girth weld root toes, where fatigue cracking often initiates and the weld width is relatively small. Finite element (FE) modeling was performed to determine a 2D Mk solution for engineering critical assessment (ECA) of a flaw at the weld root bead toe. The weld root bead profile was uniquely characterized by five variables including weld root bead width, weld root bead height, hi-lo, weld root bead angle, and weld root bead radius. Following a parametric sensitivity study, defect size, weld root bead height, and hi-lo were identified as the governing parameters. A total of 6000 FE simulations was performed, covering different combinations of weld root bead height and hi-lo. A series of automation scripts were developed in the python programming language and the Mk solution for each type of defect model was developed and provided in a parametric equation. The accuracy of the 2D Mk solutions was confirmed by the experimental data. It was found that the methods and Mk solutions currently recommended in BS 7910 and DNVGL-RP-F108 are inappropriate for assessing a flaw at a girth weld root toe.