We propose an implicit structural modeling method to generate geological models from evidences of horizons and interpreted discontinuity surfaces such as faults and stratigraphic unconformities. Our method uses a locally defined meshless interpolation to construct the implicit function. The final system to solve is therefore sparse and can be solved fairly efficiently. Discontinuities are efficiently handled with the visibility criterion, hence their management does not rely on complex conformable meshing algorithm to create a sealed mesh model. The modeling problem is formulated as a spatial regression of input data points, with bending energy penalization. This continuous energy equation is discretized adequately to the implicit function’s properties. Our method is illustrated on a synthetic cross section in 2D and a synthetic 3D model, which show its ability to build folds from sparse data in the presence of connected faults and erosions.