Mechanical properties of lithium molybdate single crystals, Li2MoO4, are studied from room temperature to 650 °C. Density functional theory calculations gave the seven elastic constants of the rhombohedral crystal at 0 K. Brillouin light scattering experiments delivered comparable values at room temperature, and measurements up to 650 °C show a linear decrease in the constants with temperature. Nano-indentation results were typical of a brittle material with a low Young modulus and allowed deriving Young's moduli, for c (63 GPa) and m (48 GPa) faces, in agreement with those computed from measured elastic constants. Compressive rupture tests were performed. At 650 °C, the rupture stress was in the range 2–7.5 MPa. No clear evidence of a plastic regime was observed before cracking, even at temperatures close to the melting point.