  We report our study of twin domains in $La_{2-x}Sr_x CuO_4$ under uniaxial
pressure. Using bulk-sensitive x-ray microdiffraction in Laue geometry, we
image the distribution of twin domains at room temperature. When compressive
uniaxial pressure is applied along one of the in-plane crystallographic axes,
the domain population changes dramatically. We observe that the twin domain
with shorter lattice parameter along the direction of pressure is unstable
under compression, and disappears completely with only moderate pressure. On
the other hand, application of tensile pressure changes the domain structure
only slightly, demonstrating the asymmetric response of the sample to uniaxial
pressure. Our observations suggest that a crystal's response to uniaxial
pressure is complex and could deviate easily from the linear-response regime.
