Atomistically detailed models of free-standing thin films of random poly(ethylene-co-propylene) were produced using a method recently applied to atactic polystyrene (Clancy, et al. J. Phys. Chem. B 2001, 105, 11493). Monte Carlo simulations of the copolymer were carried out at ethylene fractions that cover the entire range of composition investigated in a recent experimental work (Opdahl, et al. J. Phys. Chem. B 2002, 106, 5212) based on sum-frequency generation (SFG) spectroscopy. We find that there is a minor enrichment of methyl groups on the surface, as compared to the bulk composition. Interestingly, the orientation distribution of methyl and methylene units is not unimodal. For methyl units, there is about 50% probability of orientation perpendicular to the surface. The other 50% are randomly oriented. For the methylene bisector, the simulation shows that the distribution has two broad peaks at opposite angles (at 180° apart) to the surface normal. More conclusive results may be obtained by using larger sample sizes and analysis of a larger number of snapshots, both of which increase the computation time significantly. The opposite angle pairs nearly cancel each other in the computation of an average order parameter and give us a misleading net result that the bisectors are randomly oriented. With increasing ethylene fraction, the orientation distribution of methyl and methylene units tends to become more uniform; however, this change is small. The strong average orientation of methyl groups and weak average orientation of methylene groups is in agreement with experiments. However, the simulation does not show the significant relative increase in the surface methyl groups contributing to the SFG signal as compared to the bulk concentration or an increase in average orientation of methylene units, with an increase in the ethylene fraction, as inferred from the experimental results. We find that the raw experimental data obtained with an increase in ethylene fraction can be explained by the changes in the number of methyl and methylene groups on the surface rather than the increase in surface excess of the methyl groups contributing to the SFG signal, trans cancellation, and increase in orientation of methylene bisectors as deduced from the experiments.