This paper presents a method to stochastically simulate 3D karstic networks and more specifically branchwork pattern cave systems. Considering that they can be compared with 3D fluvial networks, the topological classification of Strahler and the corresponding ratios of Horton are used to define three morphometric parameters. These parameters are integrated in an algorithm that computes branches hierarchically to obtain a final network organized around the main observed inlet and outlet with a branching complexity controlled by the user. Each branch corresponds to a low-cost path between two points calculated with the 𝒜★ graph search algorithm. Speleogenetic information on inception horizons, palaeo-water tables and fractures is accounted for by adapted definitions of the searching functions of 𝒜★. The method is demonstrated on a 3D synthetic case with discrete fractures networks, inception horizons and a palaeo-water table. The simulated karsts have a realistic geometry and are geologically consistent.