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Plasma treatment of porous polymeric materials is a critical technology for creating new polymer materials that can be used in various applications. Porous polymers can be used in new approaches for creation of safe and compact hydrogen storage systems that can dramatically change existing hydrogen energy utilization. There are other potential applications for the development of new types of biocompatible and biodegradable polymeric materials for general use and for creation of new types of implants and dressing materials in medicine. Clarification of breakdown conditions of narrow discharge gaps in the micrometer region and optimization of the treatment process for different gap dimensions is the goal of this paper. The article is devoted to the experimental study of the breakdown process in the discharge gap by pulsed barrier discharge at different pressures and gaps in the region of the minimum of the Paschen curve. New approximation of the Paschen curve with the variable γ as a function of Pd, which is in good correlation with experimental results, has been proposed. A new approach is proposed for treating the inner surface of dielectric material pores with a barrier discharge, optimizing the pressure inside the pores; treating pores of a micron size requires a pressure significantly higher than atmospheric. The first results were obtained, which demonstrated the possibility of modifying the thickness of the polymer material by treatment with the barrier discharge at the time of gas pressure relief in the discharge chamber.