Gas and vapor transport properties were studied in mixed matrix membranes containing elastomeric ethylene-octene copolymer (EOC or poly(ethylene-co-octene)) with three types of carbon fillers: virgin or oxidized multi-walled carbon nanotubes (CNTs) and carbon fibers (CFs). Helium, hydrogen, nitrogen, oxygen, methane, and carbon dioxide were used for gas permeation rate measurements. Vapor transport properties were studied for the aliphatic hydrocarbon (hexane), aromatic compound (toluene), alcohol (ethanol), as well as water for the representative samples. The mechanical properties and homogeneity of samples was checked by stress-strain tests. The addition of virgin CNTs and CFs improve mechanical properties. Gas permeability of EOC lies between that of the more permeable PDMS and the less permeable semi-crystalline polyethylene and polypropylene. Organic vapors are more permeable than permanent gases in the composite membranes, with toluene and hexane permeabilities being about two orders of magnitude higher than permanent gas permeability. The results of the carbon-filled membranes offer perspectives for application in gas/vapor separation with improved mechanical resistance.