The fundamentals of oil layer drainage alone the corners of non-circular capillaries in two-phase (gas-oil) and three-phase (gas-oil-water) systems were studied. Experiments of oil layer flow along the corners of square capillaries were carried out to investigate the saturation dependency of oil phase relative permeability in single layer drainage. The quadratic behavior of oil relative permeability in the gas injection process reported in the literature was explained. For double-layer flow (water layer and oil layer) in a three-phase system, numerical analysis showed that the lubricating effect of a water layer on the relative permeability of oil phase in layer drainage was significant. The dependency of oil layer flow by gravity drainage on oil saturation saturation, water saturation, and oil-to-water, viscosity ratio was investigated numerically. The experimental results confirmed the mathematical analysis.