  The effect of uniaxial tensile stress and the resultant strain on the
structural/magnetic transition in the parent compound of the iron arsenide
superconductor, BaFe$_2$As$_2$, is characterized by temperature-dependent
electrical resistivity, x-ray diffraction and quantitative polarized light
imaging. We show that strain induces a measurable uniaxial structural
distortion above the first-order magnetic transition and significantly smears
the structural transition. This response is different from that found in
another parent compound, SrFe$_2$As$_2$, where the coupled structural and
magnetic transitions are strongly first order. This difference in the
structural responses explains the in-plain resistivity anisotropy above the
transition in BaFe$_2$As$_2$. This conclusion is supported by the
Ginzburg-Landau - type phenomenological model for the effect of the uniaxial
strain on the resistivity anisotropy.
