The recently proposed simple collision model of activated bimolecular reactions, which takes into account the nonspherical shape of molecules and includes the effects of the reagent rotation, has been extended to treat reactions of vibrationally excited reagents. Vibrational excitations are supposed to affect the reaction rates primarily through changes in the position and the height of the effective barrier. Critical dividing surfaces were calculated on the assumption of vibrational adiabaticity en route to the critical dividing surface. The positions of the adiabatic barriers as well as their heights were found to depend significantly on the choice of coordinates and the definition of the reaction path. Two approaches were considered. The analysis which gave thresholds in closest agreement with the values from quasiclassical trajectory (QCT) calculations, and which was therefore adopted in the present calculations, uses a local mode analysis along the reaction path expressed in terms of internal coordinates. Reaction cross sections were calculated for a range of translational energies for O + HCl(v = 1), O + DCl(v = 1), and O + H-2(v = 1). The results were compared with those for vibrationally unexcited reagents and both of these sets of model results were further compared with the cross sections from QCT calculations. It was evident that one significant difference between model and QCT results arises because the model only estimates "forward flux" through the chosen critical dividing surface, whereas trajectories allow for the possibility of "recrossing", thus lowering the reactive flux. Transmission factors allowing for this effect were calculated. The corrected model results are in satisfactory agreement with the QCT results although some discrepancies remain. Possible reasons for these remaining differences are discussed.