Monte Carlo simulations of xenon adsorbed on the (110) face of rutile at various degrees of coverage are reported. At low coverage adsorption is restricted to the rows along the coordinatively unsaturated Ti4+ ions. It is demonstrated that the adsorbate structure is mainly determined by the adsorbate-adsorbate interaction. As the adsorbate density increases additional "adsorption sites" appear above the superficial oxygen atoms between the rows. The nonspecific adsorption within the rows is described by a simple statistical-mechanical model of one dimensional nonlocalized adsorption of interacting particles. By use of Widom’s test particle insertion method, isotherms of adsorption are calculated and compared with experimental adsorption isotherms on rutile powder at different temperatures between 196.2 and 273.2 K.