We consider collisional excitation of H 2 molecules in C-type shocks propagating in dense molecular clouds. New data on collisional rate coefficients for (de-)excitation of H 2 molecule in collisions with H atoms and new H 2 dissociation rates are used. The new H 2 -H collisional data are state of the art and are based on the most accurate H 3 potential energy surface. We re-examine the excitation of rotational levels of H 2 molecule, the para-to-ortho-H 2 conversion, and H 2 dissociation by H 2 -H collisions. At cosmic ray ionization rates ζ 10 −16 s −1 and at moderate shock speeds, the H/H 2 ratio at the shock front is mainly determined by the cosmic ray ionization rate. The H 2 -H collisions play the main role in the para-to-ortho-H 2 conversion and, at ζ 10 −15 s −1 , in the excitation of vibrationally excited states of H 2 molecule in the shock. The H 2 ortho-to-para ratio (OPR) of the shocked gas and column densities of rotational levels of vibrationally excited states of H 2 are found to depend strongly on the cosmic ray ionization rate. We discuss the applicability of the presented results to interpretation of observations of H 2 emission in supernova remnants.