Resonant ultrasound spectroscopy has been used to measure the elastic and anelastic behaviour through known structural and magnetic phase transitions in single crystal hexagonal YMnO₃. Anomalous elastic behaviour is observed at the high temperature structural transition at ~1260 K, with a discontinuity in the elastic constants and nonlinear recovery below T<sub>c</sub>, consistent with λeQ²/<sub>s</sub> coupling. There is no change in dissipation associated with this high temperature transition, and no evidence in the elastic or anelastic behaviour for any secondary transition at ~920 K, thus supporting the thesis of a single high temperature transformation. Elastic stiffening is observed on cooling through T<sub>N</sub>, in accordance with previous studies, and the excess elastic constant appears to scale with the square of the magnetic order parameter. The strains incurred at T<sub>N</sub> are a factor of ~20 smaller than those at the structural transition, implying very weak λeQ²/<sub>m</sub> coupling and a dominant contribution to the variation in the elastic constants from λeQ²/<sub>m</sub>. The increased acoustic dissipation above T<sub>N</sub> is consistent with an order–disorder process.