This paper describes the use of mean turbulence energy closure models for the calculation of the vertical structure of the width-averaged flow due to the propagation of long waves in an open channel of constant width and rectangular cross-section. Two turbulence models were considered which required the solution of one or both of the differential equations governing the turbulence energy and its dissipation rate. Numerical solutions were obtained for the motion induced by long waves in a laboratory channel and in the Humber Estuary. The computed values of surface velocity and bed shear stress in the laboratory channel were found to agree well with observed values. The calculation procedure also accurately reproduced the vertical structure of the tidal flow in the Humber Estuary. Existing theoretical relationships for the bed shear stress under long waves were verified by the numerical calculations and a distribution of the dissipation length scale, postulated on physical grounds, was also confirmed. It was concluded that turbulence models of this type represent powerful research tools for the study of long waves, especially those which occur in nature.