In this paper we present a numerical tool to simulate dynamics of stratified sedimentary basins, i.e. depressions on the Earth’s surface filled by sediments. The basins are usually complicated by crustal deformations and faulting of the sediments. The balance equations, the non-Newtonian rheology of the sediments, and the depth-porosity compaction laws describe here a model of basin evolution. We propose numerical schemes for the basin boundary movement and for the fault tracking. In addition, a time splitting algorithm is employed to reduce the original model into some simpler mathematical problems. The numerical stability and the other features of the developed methodology are shown using simple test cases and some realistic configurations of sedimentary basins.