The over-all design of a prototype nuclear rocket is described. For practical systems using uranium-loaded graphite for fuel elements within a graphitic core structure, and hydrogen as core coolant and propellant, it is possible to achieve specific impulses of at least 800 sec. The design of the reactor core, reflector, and nuclear controls are presented for a prototype design. The nuclear, heat transfer, and fluid flow considerations for a typical design are discussed. Reactor perturbations caused by fuel element ejection, corrosion-erosion, and hydrogen density changes are discussed. Some radiation hazards are considered. Nonreactor aspects of the rocket such as hydrogen handling and the coupling of the reactor to the rocket system are indicated.