The indirect optical absorption edge in silicon and germanium has been studied in the presence of shear strain. The splitting observed in the transmission spectrum is dependent on the direction and magnitude of the applied stress and on the polarization of the light with respect to the stress axis. The results have been interpreted in terms of changes in the valence- and conduction-band structure with strain. Neglecting strain dependence of phonon energies, various deformation potential constants have been determined from the experiments. The values are: Si, 80°K: Ξu=8.6±0.2 eV, |b|=2.4±0.2 eV, |d|=5.3±0.4 eV, Ξd+1 / 3Ξu-a=3.8±0.5 eV. Si, 295°K: Ξu=9.2±0.3 eV, |b|=2.2±0.3 eV, Ξd+1 / 3Ξu-a=3.1±0.5 eV. Ge, 80°K: Ξu=16.2±0.4 eV, b=-1.8±0.3 eV, d=-3.7±0.4 eV, Ξd+1 / 3Ξu-a=-2.0±0.5 eV. An observed nonlinear dependence of the splitting on stress has been interpreted as shifts of the exciton energies with uniaxial stress. A special experimental technique using a vibrating slit in the spectrometer was used in order to obtain an accurate determination of the fine structure in the absorption spectrum.