The Teton anticline is a multiple hinge anticline containing fractured Mississippian–Devonian carbonates in the frontal part of the Sawtooth Range in Montana. The structure serves as a good surface analog for fracture patterns and connectivities within subsurface-folded carbonate reservoirs. The primary fracture sets are longitudinal and transverse relative to the axis of the fold, although two additional oblique sets are also present. The length and density of the longitudinal fracture sets are strongly controlled by position relative to multiple hinges. The transverse fractures are related to changes in fold plunge and exhibit less variation in fracture density. Fracture connectivity is dependent on the number of fracture sets, their orientations and dispersions, and the densities of the fracture sets. The connectivity is measured using two parameters: the fractional connected area (FCA), which represents the fraction of the total sample area that is connected by fractures, and the distribution of clusters of different sizes in any given area. Because the longitudinal fractures represent the dominant fracture set and also show the most variation with structural position, the fracture connectivity, as measured by both the FCAs and the distribution of cluster sizes, is greater in the vicinity of the fold hinges. The results and approaches used in the study have some important implications for subsurface-folded fractured carbonate reservoirs. The analysis of sparsely distributed fracture data from wells must be integrated with an understanding of the controls of the macroscopic structure on fracture parameters to effectively simulate fracture patterns and connectivities around subsurface structures.