This paper introduces the design and applications of integrated As₂S₃ sidewall Bragg gratings on LiNbO₃ substrate. The grating reflectance and bandwidth are analyzed with coupled-mode theory. Coupling coefficients are computed by taking overlap integration. Numerical results for uniform gratings, phase-shifted gratings and grating cavities as well as electro-optic tunable gratings are presented. These integrated As₂S₃ sidewall gratings on LiNbO₃ substrate provide an approach to the design of a wide range of integrated optical devices including switches, laser cavities, modulators, sensors and tunable filters.