Tetragonal Ba TiO3 under uniaxial tensile stress along the c axis is investigated from first principles. The structural parameters and polarization show a little abrupt change near a critical stress σc of 4.57 GPa, which is related to the uniaxial tensile stress induced change of elastic constants. We also find that the ferroelectric lattice distortion increases with the increasing stress. Moreover, it is found that uniaxial tensile stress can enhance the piezoelectric strain coefficients, which reach their maximum values at the stress σc.