The wave coupling theory with analytic solution for mutual action of optical activity and Pockels effect in birefringent crystals is developed, which is based on Maxwell's equations and the second-order polarizations responsible for the two effects. We take the crystalline quartz as an example to demonstrate the applications of the theory and some typical results for different propagation directions and different external electric fields are presented. Besides, we find out the directions of pure electro-optic delay in the optically active crystals belonging to different point groups. Along these directions both the optical activity and electro-optic coupling are absent. These will facilitate the use of an optically active medium as an electro-optic modulator
