Elastic properties of leucite have been investigated using resonant ultrasound spectroscopy over a temperature range from 300 K to 1400 K. According to these measurements, elastic moduli soften by ~50% at the Ia3d-I41/acd ferroelastic transition temperature Tc1 = 940 K relative to the value at 1400 K. A second softening is observed at Tc2 = 920 K, corresponding to the structural change from the space group I41/acd to I41/a. These elastic anomalies are analyzed in a simple model of a pseudoproper ferroelastic transition under the assumption that the transitions observed at Tc1 and Tc2 can be approximated by a single pseudoproper ferroelastic transition. The two phase transitions are accompanied by a single peak in mechanical damping attributed to the high mobility of twin walls in the intermediate phase followed by pinning in the low temperature phase. To determine whether twin walls in tetragonal leucite are polar, resonant piezoelectric spectroscopy and second harmonic generation measurements were performed but no evidence of polarity was found.