In this paper a correlation between the transport properties of poly(methyl-4-pentene-1) membranes and the supermolecular structure of polymer is demonstrated. The orientation of the amorphous regions induced by semi-crystallinity results in the appearance of the constrained and unconstrained amorphous structures. The concept of two amorphous fractions in the semicrystalline system is applied in order to better explain the transport phenomenon. Both types of amorphous fractions were found and two structural relaxations were distinguished. It was shown that the transport phenomena depended on both the free volume and the mobility of the segments creating the supermolecular structure of the membrane. The results of positron annihilation lifetime spectroscopy (PALS), calorimetric measurements (DSC) and mechanical spectroscopy (DMTA) are presented for the chosen membranes. It is tempting to believe that we should distinguish the both fractions of the amorphous phase to give better description of relaxation and transport phenomenon. Moreover, new formula and new approach to the transport process of molecules through the membrane will advance the theoretical understanding of such a process. These new concepts will also allow the better modelling of the membranes for utility purpose. Summary and analysis of the experimental data pertinent to the free volume approach are presented.