The aim of the present study is to set up a one-dimensional mathematical model, which describes the transient flow in pipelines, taking into account the influence of cavitation and free gas. The flow will be conceived of as a three-phase flow of the liquid, its vapour and non-condensible gas. The wave attenuation following transient cavitation observed by several authors, is explained taking into account the effect of gas diffusion towards individual bubbles. The possibility of shock waves is also considered. Although emphasis is placed on application of the model to pump discharge lines transporting water, the model is also suited to other types of pipelines and liquids.