Rock joints exert an enormous influence on the permeability of a rock mass because they act as interconnecting networks that provide pathways for fluids to permeate and flow within the rock structure. The apertures in rock joints are irregular in nature and induce flows that cannot be described by the parallel-plate theory based on planar joints or the classical cubic flow relationships. In this study, a two-dimensional (2D) hydraulic aperture distribution was considered to develop a mathematical model for fracture flow. In this approach, the three-dimensional Navier-Stokes equation was integrated over the joint aperture and converted to an equivalent 2D flow model. The proposed model was then solved numerically by adopting a well-known algorithm for coupling the pressure and velocity and implementing it in a computer program. The selected program is capable of predicting the deformation of the joint apertures on normal loading, the resulting flow patterns, and the volumetric flow rates associated with permeability tests conducted using a high-pressure triaxial apparatus that was designed and built at the University of Wollongong. The model output for different conditions of confining stresses and hydraulic gradients was computed, and a good agreement with the experimental results was observed.