This research aim is to develop a method for modeling the conditions for the critical hydraulic impacts emergence on thermal and nuclear power plants’ pipeline systems pressure pumps departing from the general provisions of the heat and hydrodynamic instability theory. On the developed method basis, the conditions giving rise to the reliability-critical hydraulic impacts emergence on pumps for the thermal and nuclear power plants’ typical pipeline system have been determined. With the flow characteristic minimum allowable (critical) sensitivity, the flow velocity fluctuations amplitude reaches critical values at which the pumps working elements’ failure occurs. The critical hydraulic impacts emergence corresponds to the transition of the vibrational heat-hydrodynamic instability into an aperiodic one. As research revealed, a highly promising approach as to the preventing the critical hydraulic impacts related to the foreground use of pumps having the most sensitive consumption (at supply network) performance (while other technical characteristics corresponding to that parameter). The research novelty refers to the suggested method elaborated by the authors’ team, which, in contrast to traditional approaches, is efficient in determining the pump hydraulic impact occurrence conditions when the vibrational heat-hydrodynamic instability transition to the aperiodic instability.