An attempt is made to model liquid-liquid two-phase flow inside irregular triangular cross-sectional capillaries. In a triangular capillary, the distribution of two immiscible liquids is determined by a particular threshold pressure, and the interface curvature and profile of the meniscus of the two fluids are derived and analyzed. Three hundred and sixty cases of steady-state two-phase flow were calculated using six triangular shapes, 12 contact angles ranging from 5 to , five oil-to-water viscosity ratios from 1.0 to 500, and three different tube sizes. The relative permeability curves of oil and water flow in different triangular capillaries, with different contact angles and oil-to-water viscosity ratio, can be integrated into a pair of curves. Moreover, each of these curves reveals an approximately linear relative permeability law. The results illustrate that relative permeability is independent not only of the size of the capillary, but also of its shape, meaning that relative permeability is independent of the geometry of the capillary. The results of this study reveal, for the first time, that two-phase flow behavior in the triangular cross-sectional capillaries is generally independent of the geometric property of the capillary. The detailed velocity field of flow, with different viscosities, is shown to illustrate the effect of viscosity on the velocity distribution. Modeling of the case of thin water films residing between the non-wetting phase and the inner wall indicates the presence of a lubricating effect of a low-viscosity fluid on a high-viscosity fluid at very low water saturation conditions.