Abstract We used compilations of geological and geophysical data to compare the structure, subsidence history and evolution of the Parnaíba, Michigan and Congo cratonic basins. These basins consist of 3–6 km of Paleozoic to Recent sediments and are located on thick (>150 km) lithosphere, far from plate boundaries. Sediment-corrected Bouguer gravity anomalies show that the basins are associated with a central high of up to 40–60 mGal. The high could reflect crustal thinning, but seismic refraction data suggest that the Moho is either at a similar depth or deeper beneath the basins than beneath their flanks. The seismic reflection profiles show no evidence of extensional structures in the underlying basement. We propose that the central high reflects an extensive igneous intrusion, which, on solidification, loaded the crust and lithosphere, causing a surface flexure into which sediments accumulated. Viscoelastic plate modelling of the backstripped well data shows that a subsurface load can explain the tectonic subsidence of the basins as well as some details of their internal stratigraphy, including offlap. Offlap, a ubiquitous feature of cratonic basins, can therefore be explained by tectonics in the form of flexure and does not require other controlling factors such as long-term sea-level changes.