A theoretical study of screening of excitons in semiconductors is presented. The study was motivated by a desire to improve the understanding of the optical effects of exciton screening, particularly with regard to photoreflectance experiments. The theory is based on a dielectric-function approach to the screening and thus ignores exchange contributions to the screened electron-hole interaction. To avoid having to work with retarded interactions, the region of carrier concentration for which the plasma frequency is comparable to the exciton binding energy is not treated. Away from this region the interaction can be approximated as instantaneous, and expressions for the exciton energy can be derived. In numerical application to CdS it is found that screened exciton binding energies are comparable to those obtained with a Debye-Hückel potential for the interaction. However, because the free-carrier plasma is self-screened, the band gap is a function of carrier concentration. When this is taken into account, the absolute-energy shift of excitons under screening (which is what figures in the optical effects) is much less than the binding-energy shift. In addition to the downward shift of continuum absorption due to the self-screening, the screening modifies the continuum enhancement and reduces it to unity for very high carrier concentrations.