The development of gypsum maze caves under artesian conditions has been simulated. The numerical model simulations show that the evolution of maze caves in this type of setting requires structural preferences such as laterally extended fissure networks in a horizon of the gypsum layer. Without any structural preferences vertical shafts rather than maze caves are predicted to develop. The most important stage for the development of horizontal caves under artesian conditions is found to be the initial karstification period. During this period the structure of the mature conduit system is established. The solutional enlargement of conduits is spatially extended, total dissolution rates are higher than the later ones.