The late Proterozoic to Palaeozoic evolution of the basin and basement terrains of central Australia cannot be ascribed to conventional basin‐forming models based on thermal or stretching mechanisms. Foreland basin models also are inappropriate. The principal objection to the thermal and stretching models is that the basins are not in isostatic equilibrium, whilst the foreland basin model cannot explain the quasi‐continuous evolution of the basins over periods of several hundreds of millions of years. A mechanical model is developed on the supposition that the crust has been in compression for long periods and that the evolution is determined by the balance of the compressive force, the buoyancy force, surface loading and erosion, and the elastic and viscous forces. The lithosphere is considered as a viscoelastic plate subject to a small irregular load in Late Proterozoic time. Some of the initial deflections caused by this load grow with time at a rate that is a function of the various forces and plate properties. Erosion of the uplifting areas, with the sediments deposited in the downwarps, much enhances the deformation. As bending stresses increase with time, the uplift rates increase and gravity sliding may become important. Failure by thrust faulting is also predicted, the basement being thrust over the basins. This would have occurred early in the Cambrian, corresponding to the Petermann Orogeny. The model predicts further significant deformation in the southern Arunta in Late Palaeozoic time, corresponding to the Alice Springs Orogeny and the final stages of the Ngalia Basin formation. The proposed model predicts a crustal structure that is in broad agreement with the available geophysical data and provides a framework for discussing the geological history of the basin sediments and basement metamorphics.