In this work the authors report the preparation of new addition copolymers based on 3‐trimethylsilyltricyclononene‐7 (TCNSi1) and 3,3,4‐tris(trimethylsilyl)tricyclononene‐7 (TCNSi3). A number of high molecular weight copolymers are synthesized with the content of TCNSi3 units from 5 up to 20 mol% in the presence of catalyst Pd(OAc)2/[Ph3C]+[B(C6F5)4]− with the yields of 50%–80%. The obtained copolymers are amorphous. They possess large free volume elements (R
3/R
4) based on positron annihilating lifetime spectroscopy analysis and Brunauer–Emmett–Teller surface area up to 640 m2 g−1. Permeability coefficients of the obtained copolymers are determined for a wide range of gases He, H2, O2, N2, CO2, CH4, C2H6, C3H8, n‐C4H10. The correlation between the content of TCNSi3 units and gas permeation parameters of the resulting copolymers is explored. It is found that the introduction of TCNSi3 moieties results in the rise in gas permeability of the corresponding copolymers. Moreover, increase in TCNSi3 content in the copolymer leads to an increase of gas permeability.