A new numerical method allows calculation of compaction-driven groundwater flow and associated heat transfer in evolving sedimentary basins. The model is formulated in Lagrangian coordinates and considers two-dimensional flow in heterogeneous, anisotropic, and accreting domains. Both the continuity of the deforming medium and aquathermal pressuring are explicitly taken into account. A calculation of compaction-driven flow during evolution of an idealized intracratonic sedimentary basin including a basal aquifer predicts slow groundwater movement over long time periods. Fluids in shallow sediments tend to move upward toward the sedimentation surface, and deeper fluids move laterally. The hydraulic potential gradient with depth reverses itself near the basal aquifer, and fluids in this area have a tendency to migrate obliquely into stratigraphically lower sediments. Only small excess pressures develop, suggesting that intracratonic basins are not subject to overpressuring during their evolutions. Owing to the small fluid velocities, heat transfer is conduction-dominated, and the geothermal gradient is not disturbed. Variational studies show that excess hydraulic potentials, but not fluid velocities, depend on assumptions of permeability and that both excess potentials and velocities scale with sedimentation rate. Aquathermal pressuring is found to account for <1% of the excess potentials developed during compaction. These results cast doubt on roles of compaction-driven flow within intracratonic basins in processes of secondary petroleum migration, osmotic concentration of sedimentary brines, and formation of Mississippi Valley-type ore deposits. Results might also be combined with chemical models to investigate the relationship of compaction flow to cementation in sediments.