The purpose of the research was to obtain calculation formulas for describing the flow of concrete mixtures and determining their viscosity directly in the process of vibroextrusion in regular quadrangular pyramidal channels. In solving the flow problems, it was taken into account that concrete mixtures are non-Newtonian systems in the conditions of a vibration field, and hydrodynamic theories were used to calculate the processes and rheological characteristics. Since the calculation formulas for describing the flow of fluids in a regular quadrangular pyramidal channel are absent and the channel has a square cross section, an analytical dependence was used to characterize the process, which describes the flow of a Newtonian fluid in a rectangular channel of constant cross section. The authors proposed for use simplified formulas for determining the maximum flow rate and flow rate of a Newtonian fluid in a channel of rectangular cross-section. The degree of decrease in the flow velocity and the flow rates of a Newtonian fluid in a channel of rectangular cross-section in comparison with the flow between flat parallel plates are analyzed. To describe the flow of concrete mixtures in regular quadrangular pyramidal channels, the proposed coefficients for reducing the speed and flow rate, as well as the existing formulas for the flow between flat symmetric stationary walls, which converge, were used. The possibility of using the obtained formula for the flow rate in a regular quadrangular pyramidal channel for calculating the viscosity of a concrete mixture during vibration extrusion is shown. To simplify the experimental procedure, a new formula for calculating the viscosity based on the expiration time for a certain amount of concrete mixture has been proposed. The formulas obtained are convenient for further mathematical processing and have no restrictions in their application. The proposed method for determining the viscosity expands the possibilities of studying the rheological properties of concrete mixtures in the vibroextrusion of fiber-reinforced concrete mixtures.