The vorticity equation and the first law of thermodynamics are used to construct a model which will account for the precipitation due to large-scale vertical motion. In the derivation of the model, the quasigeostrophic approximation is used; the thermal structure of the atmosphere is represented by the observed temperature at the 700-mb level and a standard stability factor; the effect of external sources of heat is ignored while that of the released latent heat is included by an approximation; orographic influences are included, and the amounts of precipitation are computed on the assumption that all condensed water falls to the earth. The model is tested on different synoptic situations in the United States, ranging from major storms with excessive precipitation to minor developments with small amounts. The orographic influences are represented by a generalized topography obtained by smoothing, and the incorporation of the effects of orography and released latent heat are found to lead to considerable improvements of the computed rainfall. On the whole, the computed patterns of rainfall agree fairly well with those observed. The major deviations are found to be due to convective currents superimposed upon the large-scale motion.