To solve the problem of excessive tensile stress of the cross-section during the cantilever casting process of high piers with inclined legs, a determination method of tensile force based on the linear programming theory and unstressed state control was proposed. Based on the internal force equilibrium method and the principle of influence matrix, the method optimized the tensile force with “stress control as the primary and alignment control as the auxiliary”. The unstressed state control method was adopted for forward iteration, and the effect of tangential displacement between segments was considered to verify the alignment of the inclined legs. Finally, a calculation process for the tensile force of buckling cables and tie rods that can simultaneously meet the stress and alignment requirements of the V-shaped pier was provided. Taking the main pier construction of a large-span continuous rigid frame bridge with V-shaped piers as the engineering application background, the linear programming theory combined with the unstressed state method was adopted to solve the tensile force for the cable-stayed buckling construction of the V-shaped pier. The variation law of the tensile force of buckling cables/tie rods during construction was analyzed, and the stress and displacement of key cross-sections were analyzed. The results show that the calculated tensile force can effectively ensure that the construction stress and alignment of the inclined legs meet the limit requirements, realizing the dual control of stress and alignment.