A theoretical analysis has been made of infrared absorption spectra measured earlier for four deep-lying sulfur centers in Si. The data consist of absorption frequencies and polarization selection rules determined for uniaxial stress applied along , , and  axes. Both ls + np transitions and ls → ls transitions are observed. The A and B centers (binding energies 0.1090 eV and 0.1872 eV, respectively) are found to be He-like, while the C and D centers (binding energies 0.3683 eV and 0.6116 eV, respectively) are found to be He+-like. The D center spectra are consistent with Td symmetry, while the A, B and C spectra are consistent in most respects with C3v or D3d symmetry. One noteworthy result is the finding that the ls + np spectral frequencies observed under stress for the A center are consistent with a ls(E) ground state.