The study is aimed at performing calculated substantiation of the thermal reliability of a pressurized water reactor (PWR) with spherical fuel elements, commonly known as a fixed-bed nuclear reactor, and determining the most advantageous design of the spherical packing from the view point of thermal hydraulics. Spherical fuel elements have a number of advantages over cylindrical fuel rods; in particular, they feature better retention of fission products, enhanced nuclear safety (due to a high melting temperature of ceramic materials), more intense heat transfer due to increased coolant flow turbulence, and a reduced influence of thermal cyclic loads on fuel elements. To confirm these statements, a thermohydraulic calculation of the KLT-40S type reactor with a modified intra-channel filling of fuel assemblies (FAs) consisting of spherical fuel elements was carried out. To determine the optimal spherical filling, two types of spherical packing were calculated, with three different diameters of spherical fuel elements. In the course of the calculation, solutions to the following issues were proposed: how to take into account the channels flow area variability, how to calculate the Reynolds number for channels of a given shape, what formulas should be used to determine the Nusselt number, and how to determine the hydraulic resistance in the channels. As a result of the calculation, data on the following main thermohydraulic characteristics have been obtained: surface heat flux density, heat transfer coefficient, maximum fuel temperature, and hydraulic losses. These results were compared with the results of calculations for cylindrical fuel rods. The obtained results demonstrate the advantage of spherical fuel elements over cylindrical fuel rods in a number of basic parameters, which gives prospects for further study of the use of spherical fuel elements in reactors of this type. The obtained study results can be applied in designing reactor plants of low and medium capacity, as well as in modernizing the existing reactor plants.