A computational model of an open-cycle gas core nuclear rocket (GCR) is developed. The solution is divided into two distinct areas - thermal hydraulics and neutronics. To obtain the thermal-hydraulic solution, a computer code is written that solves the Navier-Stokes, energy, and species diffusion equations. The two-dimensional transport code TWODANT is used to obtain the neutronics solution. The thermal-hydraulic and neutronic models are coupled, and the solution proceeds in an iterative manner until a consistent power density profile is obtained.Various open-cycle GCR designs are evaluated. First, it is assumed that the fuel and propellant do not mix. In this ideal case, it is found that the limiting factor in determining thrust and specific impulse is the maximum allowable wall heat flux. Following this simplified study, the results from a complete thermal-hydraulic/neutronic solution are presented, and the use of alternate fuels and propellants is considered. Next, a parametric design study is conducted that examines the rocket performance of the open-cycle GCR as a function of various design and operational parameters. It is found that fuel containment is very adversely affected by high reactor power or rocket acceleration. Finally, some concepts are discussed that could help improve fuel containment.