We have tested the performance of a previously developed ab initio potential in the simulation of crystalline phases. First, the model was validated by performing energy minimizations for the experimental crystal structures of several small organic molecules such as hydrocarbons, ethers, alcohols, and carbohydrates. Generally, the experimental structures were maintained very well. Calculated packing energies were in good agreement with experimental heats of sublimation. For flexible molecules, change of the molecular charge distribution with conformation was seen to be important. Secondly, crystal structure predictions were performed for methanol, ethanol, 1,4-dioxane, and propane. For methanol the experimental structure corresponded to the most favorable structure with one independent molecule, although a few structures with two independent molecules had a marginally lower energy. In the case of ethanol the experimental structure, which contains two independent molecules, was among the best ones, but in this case three structures with one independent molecule were slightly more favorable. For dioxane the high- and the low-temperature phase were predicted with low energy, but in the wrong order. The experimental structure of propane was predicted correctly: it corresponded to the most favorable structure in our ab initio potential. In all cases the predictions using the ab initio potentials were superior to predictions based on standard force fields.