Abstract: An interatomic potential for the ternary Ag-Cu-Sn system, an important material system related to the applications of lead-free solders, is developed on the basis of the second nearest-neighbor modified embedded-atom-method formalism. Potential parameters for the ternary and related binary systems are determined based on the recently improved unary description of pure Sn and the present improvements to the unary descriptions of pure Ag and Cu. To ensure the sufficient performance of atomistic simulations in various applications, the optimization of potential parameters is conducted based on the force-matching method that utilizes density functional theory predictions of energies and forces on various atomic configurations. We validate that the developed interatomic potential exhibits sufficient accuracy and transferability to various physical properties of pure metals, intermetallic compounds, solid solutions, and liquid solutions. The proposed interatomic potential can be straightforwardly used in future studies to investigate atomic-scale phenomena in soldering applications.