Samples of poly(trimetylsilyl norbornene) having different content of cis configurations of double bonds in the main chains were prepared by ring opening metathesis polymerization in the presence of the catalysts characterized by different stereoselectivity (Re2O7, RuCl3, WCl6). It was shown that the polymer obtained in the presence of the WCl6 catalysts having the closest content of the cis- and trans-configurations is distinguished by largest gas permeability, diffusion, and solubility coefficients. Determination of the parameters of gas sorption isotherms and estimation of free volume using group contribution and positron annihilation methods allowed to conclude that microstructure of this polymer (cis/trans ratio) affects its free volume and, therefore, its transport and thermodynamic properties.