A modified drift-flux model was developed for analyses of multi-dimensional, multi-phase, multi-component flows. The model enables us to apply the conventional drift-flux model to such complex flows by treating various forces acting on a dispersed phase as the effect of a generalized acceleration field, or modified gravitational acceleration field. This includes the effect of accelerations due to different forces such as a centrifugal force due to curvatures of streamlines, and a force due to inter-phasic interactions, assuming that there is no distinction among them. A general theory of the modified drift-flux model was described modeling the drift velocity for various multi-phase flow conditions, and discussions were made on possible ways to employ the theory. Applications of the present model to a gas-liquid and a particle-gas-liquid flows showed encouraging results.