Elastic and anelastic properties of a ceramic sample of elasticoluminescent SrAl2O4:Eu have been characterized as a function of temperature by resonant ultrasound spectroscopy. Both the bulk (K) and shear (G) moduli show changes attributable to the influence of the P6322→P63 (3A)→P21 sequence of structural phase transitions. Softening of K and stiffening of G at the P6322→P63 (3A) transition (Tc≈1135 K) is consistent with weak strain/order parameter coupling and tricritical character. In marked contrast, the first order P63 (3A)→P21 transition near 930 K is accompanied by stiffening such that G is ∼50% larger at room temperature than the value for a P6322 structure extrapolated directly from high temperatures and K is ∼15% larger. Softening of G at high temperatures is consistent with the existence of a soft acoustic mode. Both the P63 (3A) and P6322 phases show an increasing acoustic dissipation with increasing temperature and there is an additional peak in the dissipation behavior below ∼650 K. Landau theory has been used to analyze the overall strain and elastic behavior of SrAl2O4:Eu. The stability of the P21 structure is considered in terms of coupling between order parameters with Γ6 and M2 symmetry, though it could also be stabilized by pairwise coupling of order parameters corresponding to irreps Γ4+M2, Γ4+M3, Γ6+M3, and M2+M3. Twin walls in this material should have interesting properties, which are quite distinct from those of the bulk material and could contribute differently to the elasticoluminescent properties.