Some molecules change shape upon receiving photons of certain frequencies, but here we study light-induced deformation in ordinary dielectrics with no special optical effects. All dielectrics deform in response to light of all frequencies. We derive a dimensionless number to estimate when light can induce large deformation. For a structure made of soft dielectrics, with feature size comparable to the wavelength of light, the structure shapes the light, and the light deforms the structure. We study this two-way interaction between light and structure by combining the electrodynamics of light and the nonlinear mechanics of elasticity. We show that optical forces vary nonlinearly with deformation and readily cause optomechanical snap-through instability. These theoretical ideas may help to create optomechanical devices of soft materials, complex shapes, and small features.