Order parameter coupling associated with the first order, improper ferroelastic (Pm3 ̅m - Pbam) transition at ~510 K in PbZrO3 has been analysed from the perspective of strain and elasticity. Formal treatment of spontaneous strains using lattice parameter data from the literature reveals typical coupling with the order parameter for octahedral tilting, QR, and stronger coupling with the order parameter for antiferroelectric displacements, Q. These indicate that coupling between the two order parameters via common strains is not only biquadratic, QR2Q2, but may also have contributions from a higher order term, QR2Q4. Variations of elastic and anelastic properties obtained by resonant ultrasound spectroscopy (RUS) at frequencies in the vicinity of 1 MHz show softening as the transition point was approached from above, discontinuous stiffening at the transition point and a pattern of further stiffening in the stability of the orthorhombic structure. Below the transition point, the pattern of stiffening resembles the evolution of QR2 and Q2, as is typical of coupling dominated by terms with the form e2Q2, where e is a spontaneous shear strain. The absence of softening due to terms of the form eQ2 implies that the relaxation time for changes in the order parameters in response to an induced shear strain is slower than ~10-6 s. Also in contrast with measurements from the literature made at lower frequencies, no evidence for mobility of ferroelastic domain walls was observed at RUS frequencies. A peak in acoustic loss observed at the transition point and precursor softening in the stability field of the cubic phase are consistent with evidence for local dynamical polar clusters. Apart from some differences in relaxation times, the antiferroelectric transition in PbZrO3 does not appear to be overtly different from ferroelectric transitions such as occur in BaTiO3.