Models are presented of flexural plate basement motion (elastic, plastic-elastic and thermo-elastic) due to: (1) compressive or extensional stress; (2) variation of lithospheric basement density along the flexural plate; (3) spatial variations of plate rigidity; and (4) variations of initial plate angle, hinge point position, plate length, initial end load and plate curvature. A non-linear inverse method determines parameters. Synthetic test results and a case history from the Central Chukchi Basin illustrate the accuracy and resolution of the inversion procedure. The Central Chukchi Basin has an unloaded geometry mainly controlled by a Palaeozoic fault system. Plastic or thermal effects produce a narrow unloaded basin geometry not conforming to the Paleozoic fault distribution or to the isopach map of the Upper Ellesmerian sediments. Inverse elastic model results agree with both the known fault system development (from seismic data) and the direction of the Brooks Range motion.