During the expedition of cruise 81 on R/V Akademik Mstislav Keldysh in 2020, extensive material, representing columns of bottom sediments up to 6 m deep in the Kara Sea, was selected. After the lithological description of the columns, sediment samples were taken from the different horizons for degassing of pore gases. The extracted gas samples were analyzed for the content of the main gases, such as methane (CH4), carbon dioxide (CO2), and light hydrocarbons. The characteristic features of changes in the CH4 and CO2 content with the depth of the bottom sediments at station 6879 (the Kara Sea shelf) were studied. A model of gas diffusion was constructed taking into account the biochemical reactions of methanogenesis and methane oxidation. The rate of methane formation can be estimated by the value J ≈ 3 × 10−10 μg s−1 L−1 (per liter of sediment). The coefficient of rate of methane consumption by microorganisms is K ≈ 0.5 × 10−10 s−1. The methane flow from the bottom surface of the Kara Sea near station 6879 is q ≈ 3.47 × 10−1 μL m−2 yr−1.