Tailor-welded blank is one of the promising technologies in the application of lightweight materials for auto body parts manufacturing. The material discontinuity across the weld line results in an inhomogeneous deformation and weld line displacement. In this study, a two-dimensional analytical model is proposed to predict the tension distribution along the cross section. An energy method is used to calculate the restraining force due to bending, sliding, and unbending phenomena on the die and punch radii. To control the weld line movement, a blank holder force control strategy is proposed to achieve force equilibrium at the bottom of the part across the weld line. Finite element simulations are performed to study the effect of die and punch radii, friction coefficient, thickness ratio, and blank holder forces on the weld line displacement in strip drawing process. Under a uniform blank holder force, the weld line moves toward the thicker/stronger side implying a higher blank holder force is required for the thinner/weaker side. The results show that the weld line displacement can be controlled by an appropriate blank holder force adjustment. In order to control the weld line movement in square cup deep drawing, blank holder force on the thinner side is increased and its influences on the deformation process are investigated. Comparisons of material draw-in, weld line movement, and forming force show a good agreement between the theoretical, numerical, and experimental results.