We present the results of a Monte Carlo simulation study of adsorption from binary vapour mixtures on a solid surface using an isobaric method. The systems studied are models of simple mixtures adsorbed on a graphite surface. The interactions are modelled via Lennard-Jones 12–6 potentials, with the 10–4 potential used to describe interactions with the surface. The principal results of the calculations are the component molecular density distributions as functions of distance from the surface, from which information about selective adsorption can be obtained. These are studied for various states as the bulk composition changes at constant temperature and pressure. The states chosen are subcritical temperatures and pressures below the dewpoint pressure of the bulk mixture. The pure-component adsorption isotherms over a range of pressures from the Henry's law regime up to saturation are also determined. The mixture results are compared with the predictions of selective adsorption based upon (i) Henry's law, (ii) ideal adsorbed solution theory and (iii) a two-dimensional equation-of-state theory.