Spot weld made by resistance welding has been widely used in joining two or more overlapping sheet metal of auto body since 1950’s. Predicting failure of spot weld joints is essential for applying lightweight and efficient design of the auto body. In this paper, in order to predict the failure load of spot welds, the elliptical failure curve was proposed using the lower bound limit analysis. Based on the lower bound limit analysis, the elliptical failure curve predicted the lower bound of experimental failure load regardless of material properties and thickness of the sheet. However, the elliptical failure curve based on failure criterion using the lower bound limit analysis underestimated the failure loads of spot welds. Thus, in this study, the elliptical failure curve fit into experimental results using a nonlinear least square method. Also, the coefficient of failure curve was compared with the elliptical failure curve of failure criterion.