A model of the lithosphere, incorporating both dynamic and thermal processes, has been developed by solving a coupled system of differential equations governing stress and temperature in a 2-D block-structured geophysical medium. Designed to study the roles of tectonic and geothermal factors in continental rift formation and evolution, the model incorporates syn-sedimentary and/or erosional faulting of an upper crustal layer and allows the thermal regime of the lithosphere to be calculated through time. The method has been applied to the formation and evolution of the northwest Dnieper-Donets Basin (DDB) along one regional profile controlled by seismic and other geophysical and subsurface data. The results are compared with those published earlier for the same profile using different methods of modelling the rift and early post-rift development of the region. The final basement geometry at the end of the rifting stage predicted by the new model satisfactorily corresponds with geological data and is qualitatively similar to that predicted by the previously published models. However, the new results imply an important role for an active mechanism during rifting that generates greater mantle thinning than crustal thinning and elevated temperatures in the upper mantle beneath the rift.