Abstract: Numerical simulation or evolutionary history of an oil and gas-bearing basin is to repeat geological and thermodyanomic history of basin evolution on a computer and then to quantitate petroleum generation,accumulation and migration.The mathemat-ical model describing geological and thermodynamic history of the basin evolution ischaracterised by an initial-boundary value problem of a system of nonlinear partial dif-ferential equations. In the present paper, a numerical method for three-dimensionalproblem and the analysis of its stability are established and a numerical result for apractical model is given, which shows that the abnormal pressure and paleo-temperat-ure computed are reasonable and display physical characteristics clearly as well.

Key words: Hamiltonian system, fictitious crack model, semi-analytical finite element method, oil- and gas-bearing basin, basin evolution, mathematical model, numerical simulation