An original computational technique to generate close-to-equilibrium dense polymeric structures is proposed. Diffusion of small gases are studied on the equilibrated structures using massively parallel molecular dynamics simulations running on the Intel Teraflops (9216 Pentium Pro processors) and Intel Paragon (1840 processors). Compared to the current state-of-the-art equilibration methods this new technique appears to be faster by some orders of magnitude. The main advantage of the technique is that one can circumvent the bottlenecks in configuration space that inhibit relaxation in molecular dynamics simulations. The technique is based on the fact that tetravalent atoms (such as carbon and silicon) fit in the center of a regular tetrahedron and that regular tetrahedrons can be used to mesh the three-dimensional space. Thus, the problem of polymer equilibration described by continuous equations in molecular dynamics is reduced to a discrete problem where solutions are approximated by simple algorithms. Practical modeling applications include the construction of butyl rubber and ethylene-propylene-dimer-monomer (EPDM) models for oxygen and water diffusion calculations. Butyl and EPDM are used in O-ring systems and serve as sealing joints in many manufactured objects. Diffusion coefficients of small gases have been measured experimentally on both polymeric systems, and in general the diffusion coefficients in EPDM are an order of magnitude larger than in butyl. In order to better understand the diffusion phenomena, 10,000 atoms models were generated and equilibrated for butyl and EPDM. The models were submitted to a massively parallel molecular dynamics simulation to monitor the trajectories of the diffusing species. The massively parallel molecular dynamics code used in this paper achieves parallelism by a spatial-decomposition of the workload which enables it to run large problems in a scalable way where both memory cost and per-timestep execution speed scale linearly with the number of atoms being simulated. It runs efficiently on several parallel platforms, including the Intel Teraflops at Sandia. There are several diffusion modes observed depending if the diffusion is probed at short time scale (anomalous mode) or long time scale (normal mode). Ultimately, the diffusion coefficient that need to be compared with experimental data corresponds to the normal mode. The dynamics trajectories obtained with butyl and EPDM demonstrated that the normal mode was reached for diffusion within one nanosecond of simulation. In agreement with experimental evidences, the oxygen and water diffusion coefficients were found larger for EPDM than butyl.