In this paper a dynamic two-dimensional two-phase flow model for a single variable aperture fracture is developed. The model is based on a finite volume implementation of the cubic law and the conservation of mass for each liquid. The two-phase fracture flow system is represented by incompressible parallel plate flow within two-dimensional subregions of constant aperture. The fluid phase distribution is represented by an explicit definition of the phase presence at each location within the domain. To achieve this definition, a phase distribution is assigned to each fracture subregion. Knowledge of the phase distribution allows calculation of interface capillary pressure based on the fracture aperture. One-dimensional analytic solutions for two-phase flow are developed and used to verify the model's behavior in one dimension. The model is verified against the Sandia Waste-Isolation Flow and Transport III model for the case of two-dimensional single-phase flow. Two-dimensional two-phase flow verification is performed qualitatively because no suitable analytic or physical model is currently available. Two-dimensional flow phenomena are investigated for variable aperture fractures generated using geostatistical methods. Results from these simulations illustrate the flow processes of phase isolation, pinching off of nonwetting phase globules, nonwetting phase refusal at the edges of tight regions, and downslope migration of a fluid countercurrent to flow of a less dense fluid. ¿ American Geophysical Union 1993