There are many examples of flow of gas, with or without solids, where an abrupt change of cross-sectional area has to be implemented. A typical example is long distance pneumatic conveying where single bore pipeline normally requires high pressure drop which consequently results in high gas and solids velocities towards the end of pipeline. In these cases, stepped pipeline is used in order to reduce both gas and solids velocity whenever they reach unacceptable level. The flow structure through an abrupt enlargement of a conduit can be very complex, specially in the case of gas-solids flow. Both velocity and pressure fields are very important for the analysis and design of the overall flow characteristics. The compressible flow of gas through an abrupt enlargement was modelled using both a 1-D analytical model and 3-D numerical model. A summary of the analytical 1-D model of compressible flow through an abrupt enlargement and the results obtained for the flow through stepped pipe (81 to 105 mm) for several flow conditions are presented in this paper. Those results have been compared with the 3-D numerical model which solves basic conservation equations and very good agreement was found. Finally the same 3-D numerical model was applied to several regimes of gas-solids flow in order to investigate the structure of gas and solids velocity field, as well as pressure distribution along the pipe. Special attention has been paid to the pressure recovery downstream from the enlargement due to its important role in the design of stepped pipeline pneumatic conveying system.