[en] A brief survey of some problems appearing in designing rod-bundle Fuel Assemblies of supercritical water reactors' cores is presented. Those problems concern both getting appropriate coolability of core fuel elements, satisfactory neutron balance in the core and assurance of mechanical stability of fuel elements and other Fuel Assembly structures. Different impacts of thermodynamic and kinematic properties of supercritical water and their fluctuations in area of pseudo-critical transition upon behavior of fluid-dynamics and heat transfer are considered and discussed. It is shown incorrectness of application of the 'heat transfer coefficient' concept to supercritical flow regions, where there is a strong dependence of water properties on enthalpy and pressure. Different wide-spread turbulent models are considered from point of view of their applicability to simulating of supercritical fluid-dynamics in area of pseudo-critical transition. Principle need of account of coolant compressibility as well as turbulent exchange by momentum and energy due to density fluctuations in numerical simulation of supercritical fluid dynamics is discussed. (author)