Recently, the development of electronic technology towards higher frequencies and larger band widths has led to interest in finding new piezoelectric materials, which could be used to make filters with larger pass band widths and oscillators with better frequency stability. Langasite (La3Ga5SiO14, LGS) and its isomorphs have enticed considerable attention of researchers as a potential substrate material for piezoelectric device applications because of its high frequency stability and fairly good electromechanical coupling factors for acoustic wave devices. Nonlinear effect including drive level dependence, mode coupling, force-frequency effect and electroelasic effect are critical for the design of these devices. Third-order elastic constants (TOEC) play an important role in a quantitative analysis of these nonlinear effects. In particular these elastic constants are of great importance when the BAW (Bulk Acoustic Wave) and SAW (Surface Acoustic Wave) sensors of force, acceleration and so on are designed. Until now Langasite (LGS) and Langatate (LGT) crystal resonators have been qualified in terms of quality factor, temperature effect, isochronism defect and material quality. One of the most important advantages of those crystals is that they will not undergo phase transitions up to its melting temperature of 1450°. Presently there is no data on TOEC of LGT …