1. A physical substantiation of the dimensionless group Mr as a parameter of the resistance of the channel to erosion is given and other dimensionless groups (the flow-channel system) are included in it. 2. New dimensionless groups (6)-(9), which are a development of the Lokhtin-Velikanov idea about the law of interaction of the flow and channel, are proposed for characterizing the channel shape. 3. Equations (17)-(20) are suitable for estimating the hydraulic parameters of a stable channel. By means of these equations the values of the lower limit of the canal channel shape parameter are determined. 4. Equations (25)-(26) when I>Isb serve together with the equations of motion of water, continuity, and channel deformation for determining the hydraulic parameters of the canal during general erosion. 5. If the technical and economic calculations for individual variants when Cc≥ 20,000 Pa do not permit taking the recommended values of the lower limit of parameter B, then it is recommended to use the values of\(\tilde B\) from Table 1 depending on the type of soil with respect to the plasticity index, in which case the permissible value of the maximum depth is estimated by Eq. (29). 6. When the condition I=const