The sorption of alkanes (methane, ethane, propane, and n-butane) and alkane mixtures in poly[1-(trimethylsilyl)-1-propyne] (PTMSP) has been studied by means of Grand Canonical Monte Carlo (GCMC) simulations at low pressure. Sorption isotherms for the four alkanes in PTMSP were obtained by fixed-pressure GCMC simulation at several temperatures. The sorption isotherms followed dual-mode sorption behavior, often observed for gases and some vapors in glassy polymers; however, sorbate concentrations were consistently lower than experimental values with increasing pressure. On the other hand, solubility coefficients calculated by extrapolating the ratio, cell loading/p, to zero pressure were in good agreement with those reported from gravimetric measurements. Heats of sorption determined from plots of simulation solubility coefficients against reciprocal temperature were large and negative and, at least in the case of methane where data was available, there was good agreement with experiment. In the case of the alkane mixtures, GCMC simulation showed that the more condensable component was preferentially sorbed. The high free volume and large free-volume distribution which contribute to the high solubility of gases in PTMSP were investigated by the Voorintholt method. The large fractional free volume of 0.35 obtained from this simulation was consistent with positron annihilation measurements and with Bondi group contribution calculations. Simulation views of the free volume sites revealed a broad distribution of small and large elements.