Surface-shape-related and seismic discontinuity attributes are two different ways to delineate faults and fractures, such as curvature and coherence. These two categories of attributes have their respective advantages, depending on the seismic data, in characterizing faults and fractures. Curvature falls into the former category, and it is powerful and popular for predicting fracture densities. Another use of curvature is identifying and mapping individual faults and fractures; in this case, a quadratic surface is used for fitting the faulted horizon in a least-squares sense. But the surface shape of a faulted horizon is closer to a cylindrical surface with a cubic curve as its directrix, rather than a quadratic one, which implies that we have an opportunity of using a higher order derivative to reveal more subtle faults and fractures. I prepared a cylindrical surface-based algorithm as an aid to delineate faults and fractures. This method made use of estimates of curvature change rate and took cylindrical surface into account, and it improved delineations of faults and fractures. The applications of the new attribute demonstrated that it can detect more subtle faults and fractures than traditional seismic curvatures, especially for characterizing faults with small throws, while it smears quadratic features, such as a fold on a local scale, a dome, etc. So, the new attribute is a more targeted approach for delineating faults and fractures.