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We study radiation pressure due to Ly α line photons, obtaining and exploring analytical expressions for the force-multiplier, M F(N H, Z) = F α/(L α/ c), as a function of gas column density, N H, and metallicity, Z , for both dust-free and dusty media, employing a WKB approach for the latter case. Solutions for frequency offset emission to emulate non-static media moving with a bulk velocity v have also been obtained. We find that, in static media, Ly α pressure dominates over both photoionization and dust-mediated UV radiation pressure in a very wide parameter range (16 < log  N H < 23; −4 < log [ Z / Z ⊙] < 0). For example, it overwhelms the other two forces by |$\lower.5ex\hbox{$\,\, \buildrel\gt \over \sim \,\,$}10$| (300) times in standard (low- Z) star-forming clouds. Thus, in agreement with previous studies, we conclude that Ly α pressure plays a dominant role in the initial acceleration of the gas around luminous sources, and must be implemented in galaxy formation, evolution and outflow models and simulations. [ABSTRACT FROM AUTHOR]