The excess chemical potentials of methane, water, and ethanol in poly(dimethylsiloxane) (PDMS) and polyethylene (PE) were calculated by the Widom method. The excess chemical potentials of water and ethanol in aqueous ethanol solutions (0, 50, 100 wt %) were also calculated by the Shing-Gubbins method. The excluded volume map sampling (EVMS) method and the continuum configurational bias (CCB) method were used to increase the efficiency of sampling. In spite of the polarity and the internal degrees of freedom of the molecules, the excess chemical potentials could be calculated with a small statistical error. The solubilities of methane, water, and ethanol in the polymers were calculated from excess chemical potentials. Permeation rates calculated from diffusion coefficients and solubilities were in reasonable agreement with experimental data. The free volume cluster of each system was analyzed and was related to the permeation of small penetrants in the membranes.