We describe an exact hard-spheres scattering model for calculating the gas phase mobilities of polyatomic ions. Ion mobility measurements have recently been used to deduce structural information for clusters and biomolecules in the gas phase. In virtually all of the previous ion mobility studies, mobilities were evaluated for comparison with the experimental data using a projection approximation. Comparison of the collision integrals calculated using the exact hard-spheres scattering model with those estimated using the projection approximation shows that large deviations, over 20%, occur for some geometries with grossly concave surfaces.