Like most of the carbonate formations, the Barrois Limestones (South-east of the Paris Basin, France) are prone to karstification. At local scale, several penetrable conduits are known close to the main karst outlets, but little is known for smaller karst drainage systems. At the scale of the recharge area, tracer tests and many surface and subsurface karst features reveal a large extension of the karst drainage system governing flow and transport in the whole aquifer, but its exact geometry is also unknown. This lack of information is the main factor limiting the use of physically-based models of flow and transport for most karst aquifers. A method able to simulate possible karst network geometries accounting for uncertainties at different scales is thus required. While several methods have been proposed in the literature, none of them have been tested on a well-documented site like the Barrois Limestones. Indeed, this case study is characterized by a large amount of pluri-disciplinary data used to build a 3D comprehensive and integrative conceptual model of the whole karst aquifer, including stratigraphic and geological models, cave topographies and speleogenetic concepts, land markers of karsts, well logging and hydraulic tests, surface observations of fractures, geochemistry, tracer tests, etc. In this work, we aim at explicitly generating a set of possible geometries for the Barrois karstic network using a stochastic approach constrained by the pluridisciplinary information stored in the 3D conceptual model. After presenting the site, we propose a brief review of karstic networks simulation methods. Their applicability is discussed regarding the different scales at which we want to study the area, the corresponding data and the objectives of the associated flow simulation. First results are shown on a kilometric-scale karst subsystem in the south of the Meuse department.