  We derive an analytic expression for the intensity of resonance-line
radiation ``trapped'' in a semi-infinite medium. Given a source function and
destruction probability per scattering, the radiation pressure due to trapped
photons can be calculated by numerically integrating over analytic functions.
We apply this formalism to a plane-parallel model stellar atmosphere to
calculate the radiation pressure due to Lyman-alpha photons produced following
absorption of UV and X-rays from an AGN. For low surface gravity stars near the
AGN (g~10 cm/sec^2, r~0.25 pc), we find that the pressure due to Lyman-alpha
photons becomes an appreciable fraction of that required for hydrostatic
support. If the broad emission line emitting gas in AGNs and QSOs consists of
stellar outflows, it may be driven, in part, by Lyman-alpha pressure.
