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We have investigated the tunable lateral shift and polarization beam splitting of the transmitted light beam through electro-optic crystals, based on the Pockels effect. The positive and negative lateral shifts could be easily controlled by adjusting the permittivity tensor, which is modulated by the external applied electric field. An alternative way to realize the polarization beam splitter was also proposed by the polarization-dependent lateral shifts. Numerical simulations for Gaussian-shaped incident beam have demonstrated the above theoretical results obtained by stationary phase method. All these phenomena have potential applications in optical devices.