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A theory of the excitation of elastic waves arising from photoelastic coupling with light is presented. It is similar in character to the theory of optical parametric amplification in spatially extended media. Special attention is given to the self‐excited transient case. A novel form for the space—time development of the instability appears for the case in which the spatial dimensions of the interaction region are large compared to the distance traveled by an elastic wave during the illumination time. The predicted effects should be readily observable with existing giant pulse lasers.