It is well known that the maximum reactivity is realized for the flat fuel distribution with the fuel importance function being constant. The Lagrange method of an undetermined multiplier was used to incorporate the constraint that the mean uranium concentration or the total uranium mass shall be conserved. The OPT-SN computer program is developed, which includes an SN code ANISN-JR to solve the multigroup neutron transport equations. This program has given more reliable results than the previous scheme using the diffusion approximation, especially for bare and partially reflected fuel systems. OPT-SN was applied to criticality calculations for mixtures of 5 wt% 235U-enriched uranium dioxide and water (slurries) covered with a water reflector in all directions, in half directions, and uncovered. The calculations made for the UO2-H2O slurries in a sphere, an infinitely long cylinder, and an infinite slab with a water reflector in all directions revealed that a degree of nonuniformity effect tends to increase as the mean uranium concentration increases. It amounts to ~6% k/k for these systems at the mean uranium concentration of 4000 gU/l. The degree of nonuniformity effect is found more than 6% k/k even for as low a mean uranium concentration as 700 gU/l of the slab fuel system with a reflector only on one side. This fact confirmed from the viewpoint of nuclear criticality safety the importance of evaluating the optimum distribution of fuel in slurry contained in a tank placed on the concrete floor. Precipitation is regarded as a realistic example.