SUMMARY A mechanism of subsidence for the Williston basin is proposed and tested. The mechanism combines cooling and thermal contraction of the lithosphere with a phase transformation in the lower crust. The cooling and the phase boundary movement following a sudden change in the thermal boundary condition at the base of the lithosphere are calculated; isostatic adjustments and sea-level variations are included to determine subsidence and sediment accumulation at the basin's centre, which are compared with the data. The subsidence record could not be explained by temperature boundary conditions. The calculations show that: (1) the heat-flow boundary condition explains the long duration (more than 350 Myrs) of subsidence of the Williston basin and (2) the delay of the phase-change subsidence (about 40Myrs) explains an acceleration of subsidence in the early stages of the basin's evolution. When isostatic adjustments and the effect of sea-level variations are included, the calculated sediment accumulation history fits well the sediment record of the Williston basin.