Recent years have seen a flurry of activity in research on the use of nanoparticles to improve the properties of polymeric membranes. It is known that the change in the macroscopic properties of these hybrid materials is associated with the parameters of the cluster of incorporated nanoparticles. The percolation threshold is higher than 15 vol % for the spherical particles and decreases with the increasing aspect ratio of the embedded nanoparticles of another shape. The paper presents the results of study on the permeability of gases (N-2, O-2, CH4 and C3H8) and a test liquid (ethanol) through hybrid membranes based on the glassy polymer poly(vinyltrimethylsilane) (PVTMS) with embedded multiwall carbon nanotubes (MWCNT) with a concentration of 0.3-3 wt %. It has been found that the permeability of gases and liquids alters at MWCNT concentrations above 0.4 wt %, which corresponds to the percolation threshold for the given particles as proved by calculations. In addition, the gas permeability coefficients measured indicate a change in the transport mechanism and selectivity of the membrane.