A criticality safety study of various forms of multiplying medium based on RBMK-1000 fuel elements is presented. The calculations were performed with the Los Alamos National Laboratory Monte Carlo MCNP4B code. Continuous energy cross-section data have been taken from the ENDF/B-VI and ENDF/B-V libraries and S(,) scattering functions from the ENDF/B-IV library. A detailed three-dimensional model of the RBMK fuel element has been developed. A set of parametric calculations was performed for some hypothetical fuel conditions with the infinite model of storage lattice. Multiplying properties of homogenized mixture of fuel and moderator were also analyzed. Certain combinations of moderator (graphite-water mixture) and fuel may yield a significantly increased multiplication factor with respect to normal reactor lattice conditions. MCNP calculations were performed for fresh fuel conditions. The reduction of the multiplication factor due to burnup up to 20 GWd/TU was estimated using the WIMS/D-5 code for lattice-cell conditions. It was observed that the multiplication factor (kinf or keff) does not exceed unity if the burnup is taken into account regardless of the assumptions on the fuel conditions.