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Optimal cuts to determine the third-order elastic constants of langasite single crystals by the resonator method are proposed. By designing a small number of langasite resonators with optimal cut angles and measuring their force-frequency effects, the third-order elastic constants of langasite single crystals may be extracted separately. The numerical method to search these optimal cut angles is presented. All fourteen third-order elastic constants may be determined through a series of experimental measurements. This method will simplify traditional methods used to determine the third-order elastic constants and also will potentially produce more accurate results.