We present a geologically-based method to generate complex karstic networks. Karsts are a type of landscape formed bythe dissolution of highly soluble rocks (generally limestones). In particular, they are characterized by complex undergroundnetworks made of varieties of tunnels and breakout chambers with stalagmites and stalactites. Our method computes skeletons ofkarstic networks by using a gridless anisotropic shortest path algorithm according to field data of the underground system (suchas inlets and outlets), geomorphological features and parameters such as faults, inception horizons, fractures, and permeabilitycontrasts. From this skeleton, we define the geometry of the conduits as a signed distance function construction tree combiningprimitives with blending and warping operators. Our framework provides multiple levels of control, allowing us to author boththe structure of the karstic network and the geometric cross-section shapes and details of the generated conduits.