Geological faults, which result from rock fracturing and displacement in the subsurface, play an important role in shaping the Earth’s crust. Modeling fault surfaces and their impact on rock formations is, thus, useful for various geological applications. However, due to the complex configurations of faults, the modeling process can become difficult, requiring a framework with a specialized modeling toolkit. The primary challenge in fault modeling lies in properly correlating the geometry of faults with their effects on rock layers and other fault surfaces during displacement. To address this, we have developed a series of operators designed for fault modeling. In this manner, we present Fault-Sketch, a Sketch-Based Interface and Modeling (SBIM) framework that tackles the task of fault modeling and captures their influence on various geological structures. This framework enables the creation of surfaces as a result of rock configurations that have previously been largely overlooked in the existing literature. The collection of operators presented in Fault-Sketch are built upon a data structure fit for the purpose of consistently representing fault surfaces and their boundaries together with the influence they cause both on other surfaces and on the volumes they bound. Moreover, the operators are designed to mimic the geologic processes relevant to fault creation and displacement to facilitate their use by domain experts.