The gaseous-core or cavity nuclear reactor is of significant interest for advanced nuclear propulsion because of its high performance capabilities compared to solid-core nuclear and chemical propulsion concepts. By removal of temperature limitations associated with solid materials in the core and by use of radiative transfer as the principal mode of energy transfer from the fuel to the propellant, propellant exhaust temperatures of 7000°K and specific impulses in excess of 2000 sec can be obtained. This article describes a detailed nuclear analysis of a gaseous-core nuclear rocket engine in which the spatial effects of the cavity liner material, coolant tubes, and structural components, as well as neutron streaming out of propellant inlet and outlet (nozzle) passages, are considered. Calculational methods were evaluated, and multigroup diffusion theory was selected. Two-dimensional diffusion and transport calculations are compared for finite cylindrical cavity reactors having both central and annular nozzle exhausts. A parameter study was made of fuel and reflector materials, core and reflector dimensions, and temperature effects. Significant results of this study are: 1) extremely high fuel loadings are required for a propulsion reactor; 2) substantial preheating of the reflector will be required for startup; and 3) uranium-233 has significant advantages over 235U and 239Pu as fuel in gaseous-core nuclear rockets.