We propose a theoretical model to describe the strain-induced linear electro-optic (Pockels) effect in centro-symmetric crystals. The general formulation is presented and the specific case of the strained silicon is investigated in detail because of its attractive properties for integrated optics. The outcome of this analysis is a linear relation between the second order susceptibility tensor and the strain gradient tensor, depending generically on fifteen coefficients. The proposed model greatly simplifies the description of the electro-optic effect in strained silicon waveguides, providing a powerful and effective tool for design and optimization of optical devices.