Purpose. The research purpose is to develop a mathematical model of a pressureless flow in a channel with the occurrence in some areas of overflow layer through the wall. Using this model, it is possible to calculate the overflow layer height and length, as well as the change in flow rate in the channel due to the withdrawal of part of the fluid as a result of the overflow. Methods. The research uses a comprehensive multi-stage analytical approach. Firstly, in order to develop a mathematical model for a pressureless flow in the channel with the occurrence in some areas of overflow layer through the wall, this research analytically determines the dependence of the flow rate through the channel wall based on formulas for calculating the weir discharge coefficient. At the second stage, a mathematical model of a hydraulic mixture pressureless flow in a rectangular channel with an overflow through the wall is developed to determine the parameters and flow regimes of the stream. Findings. The dependences of the dimensionless height of the overflow through the channel wall and the effective critical flow depth on the dimensionless current channel length have been obtained for various values of the acting force parameters and the process parameter of the fluid overflow through the channel wall. This made it possible to study the dynamics of changes in these values along the channel for various values of the specified parameters, and to assess the degree of influence of the relevant factors on the characteristics of the pressureless flow along the channel and the process of fluid overflow through wall. Originality. For the first time, the model of the pressureless flow in the channel is generalized for the case of occurrence in some areas of overflow layer through the wall, when the length and height of the overflow layer are not determined by a hole in the side surface, but are controlled by a decrease in the corresponding flow rate. For the first time, this model makes it possible to calculate the height and length of the overflow layer and the change in the flow rate in the channel due to the withdrawal of part of the fluid as a result of the overflow in cases of overflowing condition of the channel with the stream under unstable and non-calculated flow regimes. Practical implications. The mathematical model and the calculation results can be used to ensure the environmental safety of the logistics systems of mining enterprises, as well as to assess the volume of the environmental pollution in case of overflowing through the wall of the channels of pressureless hydraulic transportation of waste from mineral processing and metallurgical plants.