Resonant ultrasound spectroscopy has been used to measure the complete set of elastic constants of LiKSO 4 over the temperature range of 200 to 300 K including both the hexagonal room temperature phase and the lower temperature trigonal phase. Large step changes are observed in all the elastic constants, except C 13 , at 213 K on cooling and at 243 K on warming. These step changes are associated with the hexagonal/trigonal crystallographic phase transition. The bulk modulus is approximately 15% higher in the trigonal phase than in the hexagonal phase. The hexagonal-phase elastic constants exhibit very little temperature dependence while the trigonal-phase elastic constants show a stronger dependence on temperature. The transitions are noted to be quite sluggish, taking a few hours to equilibrate. The results are described in terms of a Landau-type free energy expansion using two Ising-like order parameters with strong coupling between the two parameters. Biquadratic coupling between the order parameters and strains is shown to account for the step changes in the elastic constants as well as the temperature dependence in the trigonal phase. Coupling linear in the strains is shown to be insufficient to explain the results.