We study the predicted sub-millimeter emission from massive galaxies in a \Lambda -dominated cold dark matter universe , using hydrodynamic cosmological simulations . Assuming that most of the emission from newly formed stars is absorbed and reradiated in the rest-frame far-infrared , we calculate the number of galaxies that would be detected in sub-mm surveys conducted with SCUBA . The predicted number counts are strongly dependent on the assumed dust temperature and emissivity law . With plausible choices for parameters of the far-IR spectral energy distribution ( e.g. , T = 35 \mbox { K } , \beta = 1.0 ) , the simulation predictions reproduce the observed number counts above \sim 1 \mbox { mJy } . The sources have a broad redshift distribution with median z \approx 2 , in reasonable agreement with current observational constraints . However , the predicted count distribution may be too steep at the faint end , and the fraction of low redshift objects may be larger than observed . In this physical model of the sub-mm galaxy population , the objects detected in existing surveys consist mainly of massive galaxies ( several M _ { \ast } ) forming stars fairly steadily over timescales \sim 10 ^ { 8 } -10 ^ { 9 } years , at moderate rates \sim 100 M _ { \sun } \mbox { yr } ^ { -1 } . The typical descendants of these sub-mm sources are even more massive galaxies , with old stellar populations , found primarily in dense environments . While the resolution of our simulations is not sufficient to determine galaxy morphologies , these properties support the proposed identification of sub-mm sources with massive ellipticals in the process of formation . The most robust and distinctive prediction of this model , stemming directly from the long timescale and correspondingly moderate rate of star formation , is that the far-IR SEDs of SCUBA sources have a relatively high 850 µm luminosity for a given bolometric luminosity . Other model predictions can be tested with future studies of the redshift distribution , rest-frame UV/optical properties , and angular and redshift-space clustering of sub-mm galaxies .