The paper considers the formation of near-critical flows during operation of hydropower and water management facilities. It is demonstrated that accurately describing near-critical flows requires considering the possible presence of a non-hydrostatic pressure distribution at the initial cross-section of the flows. Failure to take this feature into account when considering near-critical flows leads to various paradoxes. The differential equation of the free-surface profile of undular near-critical flows is derived, which takes into account the mentioned non-hydrostatic factor in the initial cross-section of the flows under consideration. Integration of this equation gives solutions in the form of cnoidal waves and solitary wave. It is shown that the maximum depth of the undular near-critical flows observed under the wave tops significantly exceeds the average flow depth. The practical significance of this feature is emphasized, which must be taken into account when selecting the height of free-flow water management tunnels and pipes, determining the bottom mark of bridge girders, and assigning the height of side levees. It is proven that for a correct description of different types of near-critical flows and determination of their conditions of existence, it is necessary to consider two determining factors – the Froude number and the degree of deviation from hydrostatics in the initial cross-section of the mentioned flows. Based on theoretical and experimental studies, the conditions for the existence of cnoidal waves, solitary waves, undular jump, and other types of near-critical flows were determined.