The Chezy friction formula for steady flow in a uniform symmetrical channel with constant slope-friction factor is examined mathematically. Firstly, a wide rectangular channel and a semi-circular channel are compared in respect of the mean flow velocity using the Chezy formula with the Manning, Chezy and logarithmic laws for velocity. Then the inverse Chezy problem, i.e. the determination of the channel shape above the reference level for a given depth/discharge rating curve, is posed and the differential-integral equation for its solution is derived. The rating curves used for computation are the results of multiplying the discharge for a trapezoidal shape above the reference level by an exponential function. To facilitate interpretation of the numerical results, the relationship between side slope and discharge is analysed. It is shown by the inverse problem solution that an exponential reduction of channel flow capacity changes linear channel sides into convex sides (making the cross section shape wider) while an exponential increase of capacity causes changes into concave sides (reducing a section width) which is against common sense.