Aiming at the uncertainty of notch stress concentration coefficient caused by the change of butt joint weld shape, the related study was carried out by using parametric finite element analysis and correlation analysis. The uncertainty of weld geometry was simulated by introducing geometric changes of control points, and the correlation between control points was calculated based on a large number of test data samples generated from simulation experiments. A large number of random weld data were obtained by Monte Carlo simulation. On the basis of the notch stress method, ANSYS was used for parameterized modeling to establish a finite element model of the butt joint with introducing uncertainty in weld shape. The stress concentration coefficient of the notch at the weld toe of the butt joint was studied, and the distribution patterns under different defect levels was obtained.  The influence of weld shape uncertainty on the stress concentration coefficient of the notch was summarized. On this basis, a first-order response surface model of weld geometry parameters was established based on the large amount of experimental data. The results show that the stress concentration coefficient of the notch is positively correlated with the inclination angle of the weld toe and the height of the weld seam, while negatively correlated with the width of the weld seam. Among them, the inclination angle of the weld seam has the smallest impact.