A Lagrangian slug tracking model for dynamic gas-liquid slug flow in pipelines of varying inclinations has been formulated and implemented in C++ using an object-oriented approach. Slugs and bubbles are discrete computational objects which are coupled by exchange of mass and momentum, and organized in linked lists. The flow parameters are determined from dynamic integral mass and momentum balances on each slug and bubble. A subgrid is used in bubbles extending over pipe sections with different inclinations. Slugs and bubbles are initiated at the pipe inlet, or at low points along a pipeline, and the propagation of individual slugs are tracked dynamically, and without numerical diffusion. Some sample cases demonstrate how the structure of the Bow can be followed as it evolves from terrain effects, expansion and wake effects. These are effects that may ill some instances cause slugs to disappear and merging of bubbles during simulations. Terrain slugging computations compare well with some experimental data.