PTMSP membranes were prepared and characterized. The mean molecular weight of the polymer was found to be 450,000 La. Time dependence of the density, mechanical properties, IR spectra, DSC, PAL, and permeability data of the polymer and membranes are presented. A detailed analysis of PAL results for PTMSP samples under vacuum, in air, oxygen, and nitrogen atmosphere is presented with the aim to investigate the influence of the external atmosphere on the experimental PAL measurements and to determine correctly the size and the number of the free volume holes. From all the experimental data a model of a channel network is proposed for PTMSP with large holes (mean radium r = 0.75 nm) connected by channel-like holes (mean radium 0.45 nm). The number of large holes decreases by ageing, but not their size, whereas the number of small holes does not change but their size decreases. According to our model the decrease in the permeability of PTMSP with time could be caused by the decrease of the size of the channel-like holes.