Transient pressures subsequent to simultaneous power failure at all pumps of a multistage pumping system are analysed. Distributing pumping stations along a pipeline, rather than placing all of the required pumps within one pumping station, significantly reduces transient pressure fluctuations within the system. A computer program using the FORTRAN language is developed to analyse multistage pumping systems, with appropriate surge controls, in the event of such a power failure. These surge controls consist of valves, vacuum breakers, air chambers and reservoirs; with other controls easily added as they develop. Boundary conditions determining system controls are not developed as a part of this thesis, but are described for completeness. By comparing the maximum and minimum transient pressures occurring within- single stage and multistage systems, the premise that multistage systems give significantly lower transient pressures than single stage systems is substantiated. This reduction in transient pressures allows for possible savings in costs, as pipe wall thicknesses and the size of large, expensive control structures may be reduced. Examples demonstrating the use of the program are included.