By the time the expanding envelope of a Type II supernova becomes transparent in the optical continuum, most of the gamma-ray luminosity produced by radioactive Fe/Co/Ni clumps propagates into the hydrogen/helium envelope and is deposited there, if at all. The resulting fast electrons excite He I and H I, the two-photon continua of which are the dominant internal sources of ultraviolet radiation. The UV radiation is blocked by scattering in thousands of resonance lines of metals and converted by fluorescence into optical and infrared emission lines that escape freely. We describe results of Monte Carlo calculations that simulate non-LTE scattering and fluorescence in more than five million allowed lines of Ca, Sc, Ti, V, Cr, Mn, Fe, Co, and Ni. For a model approximating conditions in the envelope of SN 1987A the calculated emergent spectrum resembles the observed one. For the first 2 yr after explosion, the ultraviolet radiation (lambda less than or similar to 3000 Angstrom) is largely blocked and converted into a quasi continuum of many thousands of weak optical and infrared emission lines and some prominent emission features, such as the Ca II lambda lambda 8600 triplet. Later, as the envelope cools and expands, it becomes more transparent, and an increasing fraction of the luminosity emerges in the UV band.