To calculate the critical depth and the least specific energy of steady non-uniform flows in open channels, one has to solve the polynomial equations. Sometimes, the polynomial equations are too difficult to get them solved. In this study, the theory of algebraic inequality has been used to derive formulas for determining the critical depth and the least specific energy of a steady non-uniform flow in open channel. The proposed method has been assessed using examples. Results using this new method have been compared to those using other conventional methods by engineers and scientists. It is found that the proposed method based on algebraic inequality theory not only makes the calculation process to be easy, but also gives the best calculation results of the critical depth and the least specific energy of a steady nonuniform flow.