A numerical model of stratified wavy gas-liquid flow in a horizontal tube has been developed and tested with experimental data. The model solves the steady axial momentum equation together with a low Reynolds number k-epsilon model of turbulence for the eddy viscosity. The turbulence model is modified to accommodate the irregular geometry of stratified pipe flow, and the computations are performed in the bipolar coordinate system for convenient mapping of the physical domain. A set of boundary conditions for the wavy gas-liquid interface was devised from empirical considerations. Calculations of pressure drop and liquid holdup are observed to compare favourably with experimental measurements, and predicted flow quantities such as velocity and wall shear stress are also satisfactory, provided that the flow conditions at the gas-liquid interface remain steady or quasi-steady.