The electro-optical (EO) effect in transition metal oxides such as LiNbO₃ is widely used in optical modulators used in telecommunications. Recent reports pf the EO effect in BaTiO₃ thin films integrated on Si opens a possibility of creating active devices for Si photonics. The integration on Si is achived through a SrTiO₃ (STO) buffer layer. Like Si, STO is centrosymmetric, and therefore does not have a linear EO response. However, a polar phase can be stabilized by epitaxial strain. We present the results of densifty functional theory studies of the EO (Pockels) tensor in strained STO. The EO response is calculated for strains ranging from -2.0% to 2.0%. Under 1.0% tensile strain, the EO response is significant, with the largest components of the EO tensor reaching peak values of r₁₁₁ = r₂₂₂ = 505.64 pm/V. Under 1.2% compressive strain, the EO tensor has a similarly large peak of r₃₃₃ = 236.55 pm/V. These peaks in the EO response are associated with the softening of certain phonon modes as a function of strain. Our results suggest that STO grown on a properly chosen substrate can yield a very large EO response, comparable to that of BaTiO3 thin films, which is among the largest known thin-film EO responses.