Efficient and profitable production of hydrocarbons from fractured reservoirs in all stages of recovery requires that reservoir development account for the effects of compartmentalization, flow anisotropy and heterogeneity induced by faults or connected joint systems. For many years, reservoir engineers have conceptualized a fractured reservoir as a dualcontunuum (Aguilera, 1980; van Golf-Racht, 1982) A model of this type is shown in Figure 1. In this dual continuum, the matrix and the fractures are represented by separate continua with distinct properties and very regular geometry. This regularity takes the fonn of matrix blocks whose faces are mutually perpendicular, and are completely isolated from one another by the fracture continua. The fractures are also simplified. They can have up to three, mutually perpendicular orientations, and each set has unifonn fluid flow properties and very regular spacing and sizes. This extreme geometrical simplification is required in order to numerically solve the complex differential equations that are used in the simulation codes to capture such physical effects as mUlti-phase flow, imbibition, wellbore skin effects and residual saturation. In order to more accurately capture the physics of flow in a petroleum reservoir, the dual-continuum modeling approach has had to over-simplify the reservoir's flow geometry. Rock mechanics provides a perspective that is very different from the dual-continuum model prevalent in the oil industry.