We have performed elastic neutron scattering experiments under uniaxial stress σ applied along the tetragonal [100], [110] and [001] directions for the heavy electron compound URu2Si2. We found that antiferromagnetic (AF) order with large moment is developed with σ along the [100] and [110] directions. If the order is assumed to be homogeneous, the staggered ordered moment µo continuously increases from 0.02 µB/U (σ = 0) to 0.22 µB/U (0.25 GPa). The rate of increase ∂µo/∂σ is ∼ 1.0 µB/GPa, which is four times larger than that for the hydrostatic pressure (∂µo/∂P ∼ 0.25 µB/GPa). Above 0.25 GPa, µo shows a tendency to saturate, similar to the hydrostatic pressure behavior. For σ || [001], µo shows only a slight increase to 0.028 µB/U (σ = 0.46 GPa) with a rate of ∼ 0.02 µB/GPa, indicating that the development of the AF state highly depends on the direction of σ. We have also found a clear hysteresis loop in the isothermal µo(σ) curve obtained for σ || [110] under the zero-stress-cooled condition at 1.4 K. This strongly suggests that the σ-induced AF phase is metastable, and separated from the "hidden order" phase by a first-order phase transition. We discuss these experimental results on the basis of crystalline strain effects and elastic energy calculations, and show that the c/a ratio plays a key role in the competition between these two phases.