Symmetry-mode and spontaneous strain analysis has been carried out for the structural transitions taking place in Fe(1+y)Te and REFeAsO compounds on cooling from room temperature. The P4/nmm → P21/m structural transition occurring in Fe(1+y)Te is induced by a single irreducible representation E(g), indicating a pure ferroelastic transition. The increase of the interstitial Fe content hinders the displacement of the Te atoms according to the E(g) mode; as a result this mode is progressively suppressed in favour of the A(2g) mode. As a consequence the Pmmn polymorphic modification is stabilized, but in this case the P4/nmm → Pmmn transition is not ferroelastic. The P4/nmm → Cmme structural transition taking place in REFeAsO compounds is induced by a single irreducible representation B(2g), which is not active at the occupied sites. Hence, the transition is not driven by the condensation of a collective atomic displacement, but is likely characterized by a pseudo-proper ferroelastic behaviour.