Strain-induced birefringence is calculated with crystalline silicon for pressure applied along the [001] and [111] directions of the crystal. Results for the dielectric function and its change under hydrostatic strain are also given. The results are calculated for photon energies in the range 0--3.25 eV, i.e., below the direct band gap. We have made a fully-self-consistent Kohn-Sham local-density-approximation calculation, in the pseudopotential, plane-wave scheme, with a self-energy correction in the form of a rigid shift of the conduction bands of magnitude \ensuremath{\Delta}=0.9 eV. Agreement with experiment is very good in the static limit, considering disagreements among the experimental values. Values of the photoelastic tensor for [001] strain are ${\mathit{p}}_{11}$-${\mathit{p}}_{12}$=-0.118 (theory) and -0.111\ifmmode\pm\else\textpm\fi{}0.005, -0.127\ifmmode\pm\else\textpm\fi{}0.005 (expt.). For [111] strain, we obtain ${\mathit{p}}_{44}$=-0.050 (theory) and -0.051\ifmmode\pm\else\textpm\fi{}0.002, -0.051\ifmmode\pm\else\textpm\fi{}0.002 [sic] (expt.); for hydrostatic distortions, ${\mathit{p}}_{11}$+2${\mathit{p}}_{12}$=-0.067 (theory) and -0.055\ifmmode\pm\else\textpm\fi{}0.006, -0.070\ifmmode\pm\else\textpm\fi{}0.008 (expt.). For the static dielectric constant, we obtain 10.9, compared to 11.7 and 11.4 (0 K) (expt.). All experiments quoted are at room temperature, except as noted. Above 2 eV, the calculation predicts less dispersion than seen by the experiments. Thermal effects and electron-hole interactions are estimated to resolve some of the discrepancies with experiment. The experimental data for [001] strains is not consistent with a single-oscillator model, and is therefore suspect.