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 - \mathcal { R } colors using the Witt & Gordon ( 2000 ) models for radiative transfer in dusty galactic environments to arrive at the UV attenuation factors . We show that the dust in the LBGs exhibit SMC-like characteristics rather than MW-like , 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 , a _ { 1600 } \propto ( L / L _ { \sun } ) ^ { \alpha } , where 0.5 \leq \alpha \leq 1.5 . The exponent \alpha 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 - 18.5 , which is consistent with the upper limits to the star formation rate at 2 < z < 4 set by the FIR 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 .