The kinematic mass model (KMM), which has been developed to examine the dynamics of activated bimolecular reactions, has here been adapted to examine how orientational effects associated with reagent rotation influence the rotational state dependence of reaction cross-section. It is shown that, for reactions where the critical dividing surface (CDS) and the equipotential contours near to the CDS are "prolate," i.e., elongated in the direction of the longitudinal molecular axis, rotation favors impact on the CDS near collinear geometries where the barrier to reaction is least, with the result that reaction cross-sections are enhanced with increasing reagent rotation. In the case of the rotational velocity being comparable with, or greater than, the relative translational velocity, this enhancement can greatly exceed that due to part of the rotational energy being available for barrier crossing. The KMM model, allowing for this orientational effect, has been applied to the reactions O+HCl (DCl) and O+H-2 on well-known model potential energy surfaces (PESs) where both the CDSs and the equipotential contours near the CDS are prolate. The results agree well with those from trajectory calculations. The role of the above effects of reagent rotation in the case of surfaces of nonprolate shapes is discussed qualitatively.