The recently proposed simple collision model of activated bimolecular reactions which takes into account the nonspherical shape of molecules and includes the effects of reagent rotation has been studied in considerable detail, in order to determine its range of applicability. By taking the limit of hard nonspherical molecules in which the formulation becomes rigorous it is possible to show that the model is likely to work well if the shape of the potential surface is prolate in the region of the reaction barrier, as long as a direct reaction mechanism is involved. The model cannot be expected to work for diatomic reactants if the shape of the potential surface is pronouncedly oblate because of the complicated reorientation effects which such a surface exerts on the trajectories and which do not appear amenable to simple modeling. The original model is improved by including the zero-point energy corrections on the assumption of vibrational adiabaticity en route to the barrier. With the improved model, cross-sections are calculated for the reactions : H+F-2, O+H-2, N+O-2, O+HBr, O+HCl, O+DCl, and the results are compared with those of quasiclassical trajectory calculations and, in the last two cases, also with those of quantum mechanical calculations. The possible origins of the significant discrepancies which occur in some cases are also discussed.