This paper has obtained the exact analytic solutions for the cross-section curve,area and wet perimeter from the differential equation of stable channel geometry based on the fundamental assumption that particles on the channel boundary are in the threshold movement.The morphologic equations therefore are first strictly derived from simultaneous equations,including continuity equation and flow resistance formula.Comparison of the theoretical morphologic equations with measured data shows a good agreement.According to the integral mean-value theorem,moreover,another form of solution for the cross-section curve is found,which is very simple for the hydraulic computation of the stable channel.