The quadratic dependence of the rate of photodimerization of alpha-trans-cinnamic acid induced by 532 nm pulsed laser light confirms a two-photon mechanism in the single crystals. Single crystals in well-defined orientations and circularly polarized light were used in the experiments. The reaction rate deviates from first-order kinetics, but fits the JMAK expression with a coefficient indicating a mechanism intermediate between a random distribution of product molecules in the crystal and the existence of growing nuclei. The reaction is accompanied by a large change in the monoclinic beta-angle of the unit cell, corresponding to increased pi-overlap between adjacent molecules and therefore to an increased reaction rate. The improved penetration of the light in the crystal and more homogeneous product formation are significant advantages in studies of mechanisms of chemical reactions in single crystals.