This work explores the use of photoactive elastomers as elastic holographic materials. Holographic gratings were recorded on stretched films of an azobenzene elastomer, which is composed of a side-chain liquid-crystalline polymer with azobenzene mesogens, grafted to the rubbery polybutadiene block of a styrene–butadiene–styrene (SBS) triblock copolymer. The grating-formation dynamics measurements revealed the formation of two gratings of different natures resulting from the coupled mechanical and optical effects. A first grating, formed quickly upon exposure, is due to the photoisomerization of oriented azobenzene groups. A second grating, developed at longer exposure times, may originate from changes in the anisotropic structure of the SBS matrix, which is induced by the photochemical phase transition of azobenzene mesogens. The first grating is unstable, but the second grating remains in relaxed films. Both mechanisms can be enhanced by deformation of the film.