Geological restoration aims to reverse geological processes, starting from a region with its current geometry to its original configuration, prior to deformation. The geological restoration of cross-section is one of the oil and gas industry s key capabilities to aid interpretation and validation. In general, geological processes occur in a three-dimensional way. However, 3D restoration is complex and expensive and not part of the traditional workflow that emphasizes fast and efficient solutions such as restoring 2D sections. This work presents a methodology and the development of tools to map the threedimensional movement based on the restoration of geological sections. This methodology divides the problem into two steps. The first step maps the movement of cross sections to model surfaces using a surface deformer. Next, the movement of the sections together with the movement of the surfaces map the movement of the volume, here discretized in a point cloud. The numerical solution of the first step performs the movement of surfaces considering control points, restrictions imposed by the movement of cross sections together with the minimization of the tri-harmonic function in order to produce surfaces with minimum variation. The second step is the movement of the volume based on control points given by the movement of the sections added to the movement of the surfaces obtained in the first step. The development basis for these studies is the Recon-MS System, a computational system developed by PETROBRAS in partnership with the Tecgraf/PUC-Rio Institute, which, among other resources, allows the restoration of geological models, through of geometric and kinematic algorithms.