Without properly accounting for both fault kinematics and observations of a faulted surface, it is challenging to create 3D geological models of faulted geological units. Geometries where multiple faults interact, where the faulted surface geometry significantly deviate from a flat plane and where the geological interfaces are poorly characterised by sparse datasets are particular challenges. There are two existing approaches for incorporating faults into geological surface modelling. One approach incorporates the fault displacement into the surface description but does not incorporate fault kinematics and in most cases will produce geologically unexpected results such as shrinking intrusions, fold hinges without offset and layer thickness growth in flat oblique faults. The second approach builds a continuous surface without faulting and then applies a kinematic fault operator to the continuous surface to create the displacement. Both approaches have their strengths; however, neither approach can capture the interaction of faults within complicated fault networks, e.g. fault duplexes, flower structures and listric faults because they either (1) impose an incorrect (not defined by data) fault slip direction or (2) require an over-sampled dataset that describes the faulted surface location. In this study, we integrate the fault kinematics into the implicit surface, by using the fault kinematics to restore observations, and the model domain prior to interpolating the faulted surface. This new approach can build models that are consistent with observations of the faulted surface and fault kinematics. Integrating fault kinematics directly into the implicit surface description allows for complexly faulted stratigraphy and fault–fault interactions to be modelled. Our approach shows significant improvement in capturing faulted surface geometries, especially where the intersection angle between the faulted surface and the fault surface varies (e.g. intrusions, fold series) and when modelling interacting faults (fault duplex).