Data on galaxies at high redshift, identified by the Lyman-break photometric technique, can teach us about how galaxies form and evolve. The stellar masses and other properties of such Lyman break galaxies (LBGs) depend sensitively on the details of star formation. In this paper we consider three different star formation prescriptions, and use semi-analytic methods applied to the now-standard $\Lambda$CDM theory of hierarchical structure formation to show how these assumptions about star formation affect the predicted masses of the stars in these galaxies and the masses of the dark matter halos that host them. We find that, within the rather large uncertainties, recent estimates of the stellar masses of LBGs from multi-color photometry are consistent with the predictions of all three models. However, the estimated stellar masses are more consistent with the predictions of two of the models in which star formation is accelerated at high redshifts $z\gsim3$, and of these models the one in which many of the LBGs are merger-driven starbursts is also more consistent with indications that many high redshift galaxies are gas rich. The clustering properties of LBGs have put some constraints on the masses of their host halos, but due to similarities in the halo occupation of the three models we consider and degeneracies between model parameters, current constraints are not yet sufficient to distinguish between realistic models.