Polyisoprene/nanostructured carbon composites have been fabricated utilizing multiwall carbon nanotubes and carbon black nanoparticles as electrically conductive filler materials. Simultaneous measurements of (1) absorbed mass of organic solvent vapours (OSV), (2) swelling predicted elongation of sample and (3) electrical resistance changes versus the time of the presence of polyisoprene/ multiwall carbon nanotube composites (PCNTC) in the OSV ambience were carried out by an in-house computerized setup. Non-Fickian anomalous diffusion has been found for all PCNTC samples as well as for reference samples of polyisoprene/high structure carbon black composites (PCBC). Obtained results indicate that the filler material content can play a substantial role in vapour diffusion into the composite. An advanced tunneling–percolation model was developed and used for describing of the OSV sensing effect in PCNTC and PCBC.