We have analyzed several different approaches for simulating the fluid motion of a stratified two-phase system. The flow regime is transformed to a regular domain for numerical integration and the standard finite difference formulas are applied to discretize the governing and mapping equations. Five different interface iteration schemes that are based on the kinematic condition and the normal stress balance have been derived to update the position of the liquid-liquid interface. We have found that the iterative scheme based on the normal stress balance is more stable and is applicable to a wide range of capillary numbers, and that these appear to be the only sensitive parameter in the stratified two-phase system under consideration.