A study has been made of the free-molecule flow of a polyatomic gas past a body, with special reference to the evaluation of accommodation coefficients. A model of the gas-surface interaction is devised, based on the phenomenon of physical adsorption. Using this model, expressions for the thermal accommodation coefficients of the various energy modes of a polyatomic gas are developed by postulating that the energy exchange at the surface is governed by equations similar in form to the gas-phase relaxation equations. The expressions so obtained are dependent on the relevant integral heat of adsorption and the various relaxation times involved. Some suggestions are put forward as to how these relaxation times could be evaluated since, once their behaviour is known, the results of this report will provide a simple method for estimating the accommodation coefficients in a wide range of flow conditions.