We have developed a Dynamic Pore-network model for Simulating Two-phase flow in porous media (DYPOSIT). The model is applicable to both drainage and imbibition processes. Employing improved numerical and geometrical features in the model facilitate a physically-based pore-scale simulator. This computational tool is employed to perform several numerical experiments (primary and main drainage, main imbibition) to investigate the current capillarity theory. Traditional two-phase flow formulations state that the pressure difference between the two phase is equal to the capillary pressure, which is assumed to be a function of saturation only. Many theoretical and experimental studies have shown that this assumption is invalid and the pressure difference between the two fluids is not only equal to the capillary pressure but is also related to the variation of saturation with time in the domain; this is referred to as the non-equilibrium capillarity effect. To date, non-equilibrium capillarity effect has been investigated mainly under drainage. In this study, we analyze the non-equilibrium capillarity theory under drainage and imbibition as a function of saturation, viscosity ratio, and effective viscosity. Other aspects of the dynamics of two-phase flow such as trapping and saturation profile are also studied. (C) 2010 Elsevier Ltd. All rights reserved.