Exciton reflection spectra of direct-band-gap semiconductors are investigated theoretically with the aid of an appropriate model for the surface potential. The dynamics of excitonic polaritons subject to a generalized Morse surface potential and the corresponding optical response are solved exactly for the s-polarization geometry. These calculations include an analytic determination of the profiles of the electric field and the polarization vector and of the reflectivity for s-polarized light. The correlation between the parameters of this extrinsic surface potential (height at the surface, width, depth of the well, and surface damping) and the reflectance spectra is studied for the A excitons of CdS and GaAs as examples. We also analyze the manifestation of near-surface localized excitons in the reflection line shape. It is demonstrated that the excitonic bound states cause broad peaks in the spectra.