This report addresses three candidate engine cycles for a particle bed nuclear rocket; bleed cycle with uncooled carbon - carbon composite nozzle; bleed cycle with regeneratively cooled Aluminum nozzle; expander cycle with regeneratively cooled Aluminum nozzle. The analysis was performed using the SALT System Analysis Language Translator code with the following amendments; particle bed reactor was modeled as a simple heater; a regeneratively cooled nozzle model was added which includes the heating of the coolant due to hot exhaust gases and nuclear heating of nozzle. The conclusion of the analysis were the topping cycle should be pursued for Mars missions and the bleed cycle should be pursued for OTV (Orbital Transfer Vehicle) missions. This study indicates that a regeneratively cooled aluminum nozzle can be sufficiently cooled to allow its use with a PBR rocket engine. This result is based on nozzle heating due to hot exhaust gases at a maximum chamber temperature and nuclear heating effects. The highest temperatures occur at the nozzle throat, where a composite or alloy coating could protect the aluminum. Further investigation of nozzle cooling should include modeling the nozzle with more nodes, and including more accurate dimensions for the nozzle wall thicknesses and coolant flow passages. The study also indicates that an expander cycle with a cooled aluminum nozzle can operate with a high pressure PBR at realistic TPA efficiencies. Further investigation should include the improvements to the regeneratively cooled nozzle model and more accurate performance maps for the TPA components.