Understanding the mechanisms and transport phenomena of multiphase flow in porous media has great relevance in several practical applications, such as capture and sequestration of carbon dioxide, transport in fuel cells and enhancement hydrocarbon recovery. The geometry of pore space and the fluid interactions with the solid determine macroscopic properties such as porosity, relative permeabilities and capillary pressure. However, microscopic analysis provides a better description and comprehension of physical and chemical processes of fluid flow in the pore space. In this work, we developed a pore-network simulator to analyze immiscible two-phase flow for both drainage and imbibition processes. The 240×40 pore-network model has constricted capillary channels with radius on the order of 52.35 micrometer. Flow patterns and displacement efficiencies evaluation were obtained at different viscosity ratios and capillary numbers. The results, considering piston-like displacement, were similar to experiments realized previously, injecting water in an oil saturated medium. In the drainage process, the oil saturation reduces with increasing capillary number. The observed flow pattern is viscous fingerings and the front is stable with the higher viscosity ratio. In imbibition, the flow was dominated by capillary fingers at low capillary numbers. At high capillary numbers, viscous fingers were predominant and, with increasing viscosity ratio, the front presented higher stability.