A coupled continuum-pipe flow model is employed to simulate the development of karst conduits in an artesian setting, where aggressive water flows upward from an insoluble aquifer into a gypsum unit. Speleogenetic processes and controlling parameters are identified first for single conduit development. It is demonstrated that transient flow from the conduit into the surrounding fissured system of the rock enhances solutional conduit enlargement. Moreover, single conduit development is found to be highly sensitive to variations in initial diameter and hydraulic gradient. Simulating the solutional enlargement of pipe networks reveals that these two factors determine the resulting conduit pattern. Structural preferences are found to be essential for horizontal conduit development, otherwise flow paths are solely enlarged in vertical direction following the hydraulic gradient. Hydraulic gradients that increase with time can limit the extension or completely inhibit the development of horizontal caves even if lateral conduit development was structurally preferred.