We report the observation of optomechanical strain applied to thermal and quantum degenerate 87 Rb atomic clouds when illuminated by an intense, far detuned homogeneous laser beam. In this regime the atomic cloud acts as a lens which focuses the laser beam. As a backaction, the atoms experience a force opposite to the beam deflection, which depends on the atomic cloud density profile. We experimentally demonstrate the basic features of this force, distinguishing it from the well-established scattering and dipole forces. The observed strain saturates, ultimately limiting the momentum impulse that can be transferred to the atoms. This optomechanical force may effectively induce interparticle interactions, which can be optically tuned.Light-matter interactions are at the core of cold atom physics. A laser beam illuminating atoms close to atomic resonance frequency will apply a scattering force on them, and an inhomogeneous laser beam far from resonance will mainly apply an optical dipole force [1]. An intense, far detuned homogeneous laser beam does not exert a significant force on a single atom, though when applied on inhomogeneous atomic clouds, it will. This was pointed out [2] while studying lensing by cold atomic clouds in the context of nondestructive imaging.The atom's electric polarizability makes atomic clouds behave as refractive media with an index locally dependent on the cloud density. An atomic cloud thus behaves as a lens that can focus or defocus the laser beam. The atoms recoil in the opposite direction to the beam deflection due to momentum conservation. In solid lenses, this optomechanical force causes a small amount of stress with negligible strain, due to their rigidity. An atomic lens, however, deforms, making the force on the atoms observable by imaging their strain. We refer to this optomechanical force as electrostriction, since it resembles shape changes of materials under the application of a static electric field. Electrostriction can be viewed as an optically induced force between atoms, since the force each atom experiences depends on the local density of the other atoms.Optomechanical forces are applied in experiments on refractive matter mainly by optical tweezers, pioneered by [3], using structured light. Less commonly, such forces can be applied by homogeneous light using angular momentum conversion due to the material birefringence [4], or using structured refractive material shapes [5]. Optomechanical forces implemented by such techniques are used for optically translating and rotating small objects. By applying electrostriction on cold atoms we gain access to the effect of optical strain -an aspect in optomechanics not directly studied yet in spite of its importance in current research [6].Interactions between cold atoms can appear naturally or be externally induced and tuned. Tuning is mostly done using a magnetic Feshbach resonance, which was used to demonstrate many important physical effects such as Bose-Einstein condensate (BEC) collapse and explosion [7], Feshbach molecul...