The criticality constants of fissile solutions containing borated Raschig rings are evaluated using the Monte Carlo code KENO IV with various geometry models. In addition to those used by other investigators, a new geometry model, the random geometry model, is presented to simulate the system of randomly oriented Raschig rings in solution. A technique to obtain the material thickness distribution functions of solution and rings for use in the random geometry model is also presented. Comparison between the experimental data and the calculated results using the Monte Carlo method with various geometry models indicates that the random geometry model is a reasonable alternative to models previously used in describing the system of Raschig-ring-filled solution. The random geometry model also provides a solution to the problem of describing an array containing Raschig-ring-filled tanks that is not available to techniques using other models.