The numerical modeling of the Ukrainian part of the Donbas fold belt indicates that the coalification pattern was controlled mainly by the maximum burial depth of coal seams and the heat flow (HF) (40–75 mW/m2) during the Permian. The coalification pattern was overprinted by magmatic events during the Late Permian in the south syncline (150 mW/m2) and during the Permian–Triassic in the north of the Krasnoarmeisk region (120 mW/m2). The coalification pattern shows a strong increase in vitrinite reflectance values toward the east and southeastern parts of the study area likely caused by (1) an eastward increase in burial depth, (2) a probable eastward increase in HF, and, (3) probable magmatic activity. An increase in total erosion toward the eastern and southeastern parts was also observed with a maximum erosional amount of approximately 8 km (5 mi) in the southeastern part of the study area. The basin modeling of this area predicts that the main phase of hydrocarbon generation occurred during the Carboniferous–Early Permian subsidence. The magmatic events that occurred during the Permian–Triassic caused renewed pulses of hydrocarbon generation. A large amount of the generated hydrocarbons was lost to the surface because of a lack of seals. However, the numerical simulation predicts accumulations of about 2 tcf (57 billion m3) of methane generated from Carboniferous coals in the south and main synclines, where Lower Permian seal rocks are preserved. Finally, this study provides data on methane resources along the northern flank of the basin, which remains a significant frontier for natural gas exploration.