Numerical models are developed to predict the generation, accumulation, and escape of hydrocarbons at the time of sediment accumulation (basin modeling) in the West Siberian geosyneclise during the Jurassic, Cretaceous, and Cenozoic. A theoretical framework for such computer models is presented with a special emphasis on modeling of gas generation during early catagenesis. The study provides a description of the algorithm used for interpretation of simulation results and considers the stages of formation of a shale cap rock during lithogenesis. Peak oil generation began in the Aptian and continued for about 80 Myr until Eocene–Miocene times; gas generation in the late catagenetic window took place from the Valanginian to the Maastrichtian. Numerical simulations show that the major oil-prone source rocks in the South Kara kitchen area were, in the decreasing order of potential, the Bazhenovo (Yanov Stan), Kiterbyut, and Malyshevka Formations. The Upper Jurassic regional rock unit generated over 60% of liquid hydrocarbons and heterocyclic compounds (oils). The major gas-prone source rocks in the area were, in the decreasing order of potential, the Kiterbyut, Malyshevka, Alym, and Bazhenovo (Yanov Stan) Formations. The Lower and Middle Jurassic regional rock units generated about 65% of hydrocarbon gases. Results are presented to quantify the amount of hydrocarbons dissipated due to either the absence or poor effectiveness of confining seals and to explore the role of Cenozoic tectonic processes in the formation of petroleum accumulations in the basin.