A one-dimensional wave model for incompressible flows predicts the transition between the stratified and slug flow regimes in pipes. The one-dimensional wave theory contains less empiricism than the commonly used Taitel-Dukler model for this transition. The empiricism embodied in the Taitel-Dukler analysis leads to the underprediction of the transition velocity at high gas density in large pipes in particular. This paper presents a complete solution methodology for the one-dimensional wave approach for this transition and validates the method by comparison with a wide range of flow regime data at large pipe diameters, at high gas density and in horizontal or inclined pipes. The analysis is extended, by using the method of characteristics, to model wave growth, decay and interaction. Since all waves usually propagate downstream we are led to question the Taitel-Dukler model for slug frequency and to suggest that the inlet characteristics, including compliance, play a role.