Conformational properties and mobility of two polymeric chains containing 30 repeating units of either polyethylene (PE) or trans-polyacethylene (PA) confined into the channel formed by eight alpha -cyclodextrins (alpha CDs) are studied by Molecular Dynamics simulations performed at 500 K and compared with the behavior exhibited by the same chains when they stand alone in vacuum. The rotaxane structure (i.e. polymeric chains threaded into the alpha CDs channel) is stabilized with respect to the separated chain and alpha CDs mostly because of van der Waals interactions. As it might be expected, large differences are observed in the molecular characteristics of the isolated chains as compared to their confined counterparts. The differences are in the sense of decreasing the conformational mobility in favor of extended conformations in the case of confined chains. Comparison of the results obtained for confined PE and PA chains indicates a noticeably larger mobility of the PA chain. Molecular dimensions obtained for the isolated PE chain agree with the results published in the literature.