We present our analysis of UV attenuation by internal dust of a large sample (N=906 galaxies) of Lyman break galaxies (LBGs). Using spectral energy distributions (SEDs) from the PÉGASE galaxy spectral evolution model, we apply dust attenuation corrections to the G-R colors, using the Witt & Gordon models for radiative transfer in dusty galactic environments to arrive at the UV attenuation factors. We show that the dust in the LBGs exhibits SMC-like rather than Milky Way-like characteristics and that the dust geometry in these systems is most likely to be represented by a clumpy shell configuration. We show that the attenuation factor exhibits a pronounced dependence on the luminosity of the LBG, a1600∝(L/L☉)α, where 0.5≤α≤1.5. The exponent α depends on the initial parameters of the stellar population chosen to model the galaxies and the dust properties. We find that the luminosity-weighted average attenuation factor is likely to be in the range from 5.7 to 18.5, which is consistent with the upper limits to the star formation rate at 2<z<4 set by the far-infrared background. This implies that the current UV/optical surveys do detect the bulk of the star formation during the epoch 2<z<4 but require substantial correction for internal dust attenuation.