Cratonic basins form within stable regions of the continental interior and initiate during periods of break-up and dispersal of supercontinental assemblies, when the continental lithosphere may experience tensional stress. We investigate the subsidence of cratonic basins using a 1D forward model of protracted stretching at low strain rates of thick continental lithosphere. At low strain rates, subsidence history departs from the uniform instantaneous model, as supported by calculations of the thermal Péclet number. Cooling as a result of upward advection is matched by thermal diffusion, producing a subsidence trajectory with a near-constant slope and a slight elbow when stretching ceases. The model is used to evaluate the subsidence history of boreholes in cratonic basin-fills. Marked accelerations and decelerations of subsidence, attributed to secondary mechanisms such as the dynamic response to mantle convection, are removed from the backstripped, water-loaded subsidence curves to obtain the ‘reduced' subsidence. Fits to the reduced curves indicate strain rates of c. 10−16 s−1, stretching durations of 50 Ma, and stretch factors of as little as 1.1–1.3, despite the extreme longevity of subsidence. Cratonic basins are therefore part of the rift–drift suite, occupying a portion of the existence field at low stretch factors and low extensional strain rate.