  We study theoretically the variation of the magnetic and the structural
transition temperatures of the iron arsenide superconductors with external
uniaxial stress. We show that the increase of the transition temperatures
reported in recent experiments is compatible with a simple magneto-elastic
model in which the physical origin of this variation is linked to the fact that
antiferromagnetic bonds are longer than the ferromagnetic ones in the magnetic
phase. We make predictions which can be verified in order to test the relevance
of this model.
