Abstract: By taking the minimum strain energy as objective functions, three approaches for determining the optimal hanger forces of tie-arch bridges are proposed. The first one is named Stiff Hanger Method, which is based on unconstrained minimum strain energy. The second one is termed Infinite Axial Stiffness Method, based on unconstrained minimum bending strain energy. In the third approach, a quadratic programming problem is formed, in which the objective function is to minimize the bending strain energy of the discrete structure, and the constraints can be set by giving the upper and lower boundaries of bending moments for some sections, acceptable displacement at certain points and/or limits for hanger forces. As to the implementation procedure, the Stiff Hanger Method and the Infinite Axial Stiffness Method can be executed by substituting some cross-sectional areas with large enough numerical values, and the practical process for solving the quadratic programming problem is also discussed. In the end, the applications of the three methods are exemplified and discussed.