Membrane gas separation technologies (air separation, hydrogen recovery from dehydrogenation processes, etc.) use traditionally the glassy polymer membranes with dominating permeability of "small" gas molecules. For this purposes the membranes based on the low free volume glassy polymers (e.g., polysulfone, tetrabromopolycarbonate and polyimides) are used. On the other hand, an application of membrane methods for VOCs and some toxic gas recovery from air, separation of the lower hydrocarbons containing mixtures (in petrochemistry and oil refining) needs the membranes with preferable penetration of components with relatively larger molecular sizes. In general, this kind of permeability is characterized for rubbers and for the high free volume glassy polymers. Data files accumulated (more than 1500 polymeric materials) represent the region of parameters "inside" of these "boundaries." Two main approaches to the prediction of gas permeability of polymers are considered in this paper: (1) the statistical treatment of published transport parameters of polymers and (2) the prediction using model of ≪diffusion jump≫ with consideration of the key properties of the diffusing molecule and polymeric matrix. In the frames of (1) the paper presents N-dimensional methods of the gas permeability estimation of polymers using the correlations "selectivity/permeability." It is found that the optimal accuracy of prediction is provided at n=4. In the frames of the solution-diffusion mechanism (2) the key properties include the effective molecular cross-section of penetrating species to be responsible for molecular transportation in polymeric matrix and the well known force constant (ε/k)(eff i) of {6-12} potential for gas-gas interaction. Set of corrected effective molecular cross-section of penetrant including noble gases (He, Ne, Ar, Kr, Xe), permanent gases (H(2), O(2), N(2), CO), ballast and toxic gases (CO(2), NO(,) NO(2), SO(2), H(2)S) and linear lower hydrocarbons (CH(4), C(2)H(6), C(3)H(8), C(4)H(10), C(2)H(4), C(3)H(6), C(4)H(8) - 1, C(2)H(2), C(3)H(4)-m (methylacetylene) and C(3)H(4)-a (allen) is determined by using two above mentioned approaches. All of this allows calculating preliminary the permeability parameters of above mentioned gases for most part of known polymers based on limited experimental data. The new correlations suggested demonstrate that the available free volume of polymeric matrix plays an important role in providing of rate and selectivity of gas diffusion for glassy-like polymers; the rate and selectivity of gas diffusion in rubbers is affected mainly by cohesion energy density (CED) the both polymer parameters being calculated by traditional additive group contributions technique. Results of present study are demonstrated by calculation of expected permeability parameters in relation to lower hydrocarbons and some toxic gases for polynorbornene based polymers, PIM and PTMSP outlining potential of practical application for new membrane polymers.