Much research activity is carried out to reduce water consumption for domestic purposes. This leads to the possibility of reducing the amount of water introduced into building drainage systems. However, an accurate estimation of the flow attenuation within building drainage pipes is of great importance to prevent solid eposition and subsequent blockage. The research is focused on the field of subcritical flow in partially-filled pipes. Experimental and numerical investigations have been carried out to study the wave attenuation in the following configurations encountered in drainage pipe systems: i) A simple pipe, ii) A pipe subject to one concentrated lateral inflow, iii) A pipe with gate fixed at the downstream section, generating an interaction between wave and backwater profiles. In the present study the Saint-Venant equations are derived in their general and characteristic forms. A number of numerical procedures for solution of the Saint-Venant equations are reviewed, and the rectangular grid characteristics method, diffusing scheme and Strelkoff's implicit method are chosen to solve the equations. The stability of the finite-difference methods used is investigated for free-outfall and controlled outfall boundary conditions. An experimental installation consisting of 0.105 m diameter uPVC pipe is used to investigate the characteristics of the flow and to form test cases for the numerical methods. Comparisons between computed and observed depth hydrographs, peak depths and depth variations along the pipe are made for subcritical flow in a pipe of slope 1/300. The rectangular-grid characteristics method and the diffusing scheme are also applied to supercritical flow. Flow tests are undertaken for supercritical flow in a pipe of slope 1/200 to validate the use of these methods. The investigation revealed that the attenuation rate of peak depths is affected by the volume of the waves. The implicit method is the most suitable method, dealing efficiently with most problems encountered in drainage pipe systems of flat slope. The diffusing scheme can model the attenuation of supercritical flow within building drainage pipes.