Modelling the discontinuity network of fractured reservoirs may be addressed (1) by purely stochastic means, (2) with a fractal approach, or (3) using mechanical parameters describing the spatial organisation of fracture systems. Our paper presents an approach where the geometrical properties of the fracture networks are incorporated in the form of both statistical and mechanical rules. This type of approach is particularly suitable to model stratified fractured rock masses comprising two orthogonal families of joints and a family of sedimentary discontinuities. Their geometrical arrangement is governed by two kinds of rules based on (1) statistical parameters such as the mean, standard deviation of joint length and of bed thickness, both determined by field observations, and (2) geometrical parameters that result from genetic processes inferred from field observations and analogue experiments on the nucleation and propagation mechanisms of joints. Using these parameters, we generate realistic networks in terms of the relative position of joints that control the overall network connectivity: the model enables all combinations of joint spacing and vertical persistence for orthogonal patterns ranging from ladder type to grid type patterns. It also integrates the concept of mechanical “saturation” of a bed, thereby permitting the generation of both “saturated” and “unsaturated” networks.