Reaction cross sections and rate constants for the D + H-2(v = 0-1,j = 0-7) reaction have been obtained by quasi-classical, trajectory (QCT) calculations on the three ab initio potential energy surfaces (PESs) available for this system. A good agreement has been found between the QCT and quantum mechanical (QM) reaction cross sections and rate constants for the D + H-2(v = 0-1,j = 0) reactions. Thermal rate constants for the D + n-H-2(v=0) and D + n-H-2(v=1) have been calculated from the excitation functions, over a wide range of temperatures. The comparison with the quantum mechanical (QM) calculations and experimental results shows that, in general, QCT thermal rate constants are smaller than their QM and experimental counterparts, and this can be traced back to a decrease in the classical reactivity in the threshold region with rotational excitation of the reagents. In addition, the analysis of the QCT results provides an explanation for the differences found in thermal rate constants calculated on the three PESs in terms of specific features of each of these potentials.