A Reynolds stress equation model is developed to analyze the turbulence structure of fully developed open channel flows. Main emphasis is placed on the reproduction of the anisotropy of turbulence and the modeling of the effect of free surface. The pressure-strain term in the model consists of the Speziale-Sarkar-Gastki model and the Shir model for free surface effects. Through comparison on the three turbulent normal stresses and analysis of performance of the pressure-strain correlation, it is shown that the present model reasonably captures the intensified anisotropy of turbulence near free surface.