Two-phase slug flow in inclined pipelines can cause significant practical operating problems. When slugs flow in an inclined pipeline that contains sections of different inclinations, they undergo a change of length and slug flow characteristics as the slug moves from section to section. In addition, slugs can be generated at low elbows, dissipate at top elbows and shrink or grow in length as they travel along the pipe. A mathematical model and a computer program were developed to simulate these phenomena. The model was based on the sink/source concept at the pipeline connections. A connection between two pipeline sections of different slopes was conveniently called elbow. An elbow accumulates liquid as a sink, and releases liquid as a source. The sink/source has a characteristic capacity of its own. This capacity is positive if the liquid can indeed be accumulated at the elbow or negative if the liquid is actually drained away from the elbow. The hydrodynamic flow model was also used to calculate the film liquid holdup in horizontal and inclined pipelines. The model can successfully predict the liquid film holdup if the liquid film height is assumed to be uniform through the gas pocket. The overall effect of a hill or terrain on slug flow depends on the operating flow rates and pipeline configurations. For special cases of near constant slug frequency corresponding to moderately high superficial liquid and gas velocities, this effect was found to be small. The film liquid holdup decreased with increasing pipe diameter. The unit slug length increased at the upstream inclined pipes and decreased at the downstream inclined pipes with increasing pipe diameter. The possibility of pseudo-slug generation was increased at large pipe diameters even at high sink capacities. At low sink capacities, no pseudo-slugs were generated at high superficial velocities. The slug flow characteristics were more affected by low superficial gas and liquid velocities, large pipe diameters and shallow pipeline inclinations.