We combine phase space and Monte Carlo descriptions of the sputtering of diatomic molecules in the independent binary collision approximation. These apparently dissimilar models are almost physically identical, but provide in part complementary information. We consider in detail the sputtering of the molecules SiF and Kr2, assumed respectively to be strongly and weakly bound compared to the binding energy of the molecule to the substrate (in accord with experimental observation). We calculate the kinetic energy, angular, and rotational and vibrational energy distributions for both molecules. In addition, we demonstrate that significant correlations between rotational, vibrational and kinetic energy of sputtered molecules exist, and that all distributions are essentially independent of ejection angle. © 1986 Elsevier Science Publishers B. V. (North-Holland Physics Publishing Division).