Two linear combination models for the transition zone in two-dimensional incompressible boundary layers have been programmed into the commercially available computational fluid dynamics software suite of programs, PHOENICS as a sink of momentum. It has been shown that it was possible to use a laminar velocity profile to predict laminar, transitional and turbulent boundary layer parameters. Method one, attributable to Fraser, Higazy and Milne (1994), was tested against a variety of flows including zero and constant adverse and favourable pressure gradients, and also the varying pressure gradient Rolls Royce T3C flows. The method gives good prediction of skin friction and transition length when the start of transition was in zero and favourable pressure gradient flows, but the transition length was always under predicted when the start of transition was in adverse pressure gradient. Method two, attributable to Solomon, Walker and Gostelow (1995) was tested in flows where the start of transition was in adverse pressure gradient. This method will probably give an improved prediction o f transition length, but the results were highly sensitive to the properties of the flow at the start of transition. It has been shown that in order to predict the start of transition using the Abu-Ghannam and Shaw (1980) correlation, a meaningful average of free stream turbulence intensity in the flow was required. It was found that a reasonable estimate could be found by integrating the free stream intensity value from the inlet and taking the average. A new method was developed to overcome the limitations of the Abu-Ghannam and Shaw correlation, and is based on the turbulent energy equation. The method used integrated averages of properties across the boundary layer starting from the leading edge and marching downstream. The boundary layer model was coupled to the free stream by a correlation which was found, using the Rolls Royce T3A, T3A-, T3B and T3C data, to be a function of free stream turbulence intensity, dissipation length scale and pressure gradient parameter. The method was found to give good prediction of the start of transition, and hence skin friction in the favourable pressure gradient flows. Unfortunately there was not enough data to extend this correlation to adverse pressure gradients.