On the basis of a theory of the structure of W Ursae Majoris stars given in an earlier paper, a model for calculating their light curves is proposed. The most important feature of the model is the single, connected convection zone that forms the common envelope of the system. The model provides an explanation for the anomalous luminosity ratios of W UMa stars and cor- rectly predicts the major characteristics of their light curves. A maximum of 1.28 mag for the depth of primary minimum in integrated light is also predicted and shown to be consistent with the observational data. However, the asymmetries in the light curves of many systems cannot be explained with this model. Furthermore, primary minimum for the theoretical light curves is due to the eclipse of the more massive component, which is not true for the majority of observed systems