The article deals with the issues related to the modelling of unsteady fluid flow in short and long pipelines, including various equipment: pumping stations (equipped with cen-trifugal or piston pumps), valves of different operating principle, pressure stabilizers, etc. Pres-sure stabilizers (especially in short pipelines) are able to protect the pipeline from sudden pres-sure surges. This is important not only in terms of the strength of the pipeline system, but also in short pipeline circuits for a uniform flow of liquid fuel supply. As a mathematical tool for numerical solution of differential equations of quasi-hyperbolic type, the method of character-istics is applied, which allows to consider the problems that develop over time. The program is written in C++ with graphical interpretation in Maple. © Published under licence by IOP Publishing Ltd.