A robust 3D model of subsidence coupled with channeling into salt formations was developed. Its architecture allows easy implementation of empirical phenomenological laws regarding channel formation and subsidence within a formation. The model can be used to perform fast and adapted-to-complexity computations where data are sparse in time and space and where extensive state-of-the-art measurements are not available; as a preliminary model, it could ideally guide the development of more sophisticated, heavily parameterized and resource-demanding codes. Sensitivity analyzes on several 2D and 3D parameterizations were performed to assess the influence of several parameters in determining the shape of subsidence. The 3D finite element model coupling flow (using Darcy's law) and subsidence (empirical models) was then tested for a French nineteenth century salt mining site, where mining may have induced subsidence by disrupting the balance between fresh water and brine. A sensitivity analysis was conducted to assess the impact of flow parameters or subsidence on results.