A procedure is developed that systematically matches observations of plate flexure and gravity anomalies at simple convergent boundaries to the bestfitting two-dimensional flexural geometry obtained by a thin elastic sheet of specified elastic strength. The procedure allows analytical solution for three independent variables, one of which is the initial (preflexure) elevation of the reference surface and two of which are related to the vertical forces and bending moments that act on the plate. Application to four profiles constructed across the Apennine convergent system in Italy shows that the observed depth of the basal Pliocene surface (which marks the base of the foredeep basin) and the observed Bouguer gravity anomalies can be fit by a two-dimensional elastic plate model with an effective elastic thickness of about 20 km on three profiles and about 10 km on the fourth profile. The initial elevation, prior to flexure, is determined to have been about 1000 m below sealevel on all profiles. Large bending moments and/or vertical shear forces are required to act at the effective plate ends in order to maintain the observed deflection (moments between 0.5--1017 and 3¿1017 N, and shear forces between +3¿1012 and -3¿1012 N/m). Gravity modelling indicates that, on the two northernmost profiles, these terminal forces can not be supplied by a static mass at crustal depths and suggests that, on all four profiles, the terminal forces are supplied by anomalously dense material present at depths of 75-150 km beneath and west of the west coast of Italy. This dense material probably corresponds to westward-subducted lithosphere of the Adriatic plate, extending from the northern Apennines to the southern Apennines and Calabria. This study suggests that in subduction systems, like the Apennines, that are characterized by backarc extension, forces acting on subducted lithosphere at depth can be expressed at the surface in the geometry of the foredeep basin that forms adjacent to the subduction zone. ¿ American Geophysical Union 1988