The restoration of sections involving salt structures is complicated, because it is often difficult to understand fully the dynamics of the system. The occurrence of hydrocarbons is often associated with traps in the vicinity of or directly adjacent to, salt structures; different methods to delineate the combined evolution of salt and sediments have therefore been developed. Because dynamical parameters are rarely known more accurately than within an order of magnitude, intrinsic uncertainties are introduced in any model based on assumptions concerning the dynamical behaviour of salt and sediments. A quantitative approach is presented here, guided by observed geometries of the salt-sediment interface and of the bed horizons from seismic and/or well data. This novel procedure considers the salt-sediment system as composed of geometric shapes that are allowed to vary with time when calculating the salt-sediment evolution. By letting sedimentary beds move around the developing salt structure, the influence of the uprising salt on the evolving bed geometries above and around the salt is depicted. Because the predicted present-day bed geometries must also be in accord with applied control criteria (such as the change in salt volume with time, the geometry of the depositional surface with time, and the compaction history), additional constraints are put on the parameters controlling the evolution of the salt shape. The capability of being able to follow the changing bed geometries with time allows the strain in the sediments through time to be traced The stresses that generated the deformations in the sediments can then be inferred through application of the theory of elasticity. Furthermore, the combined evolutionary picture may be used to assess thermal ＇＇focusing＇＇ through time by a highly conductive salt structure, because the salt and bed geometries are known at each instant. A case history from the North Louisiana Salt Basin shows aspects of different combinations of control criteria on salt-sediment evolution. Information is thus provided on the importance of evaluating the data and control criteria necessary for constraining the possible evolution histories. It is suggested that the novel inverse procedure presented here will improve understanding of the combined evolution of salt and sediments, and is therefore of significance in hydrocarbons exploration.