The pulsed inductive plasma accelerator allows for ionization of a cold gas propellant to plasma and acceleration of plasma with the same current pulse and without plasma contact with any part. This is beneficial since erosion is never a problem and lifetimes are limited only by the amount of carried propellant. To date, work involving the pulsed inductive plasma accelerator concept has been largely experimental with minimal computational analysis. The goal of the present research was to develop a computational tool using Maxwell’s equations coupled with the Navier-Stokes fluid equations to fully analyze a pulsed inductive plasma accelerator. A plasma model was developed using the Saha equation and partition functions to calculate all required thermodynamic properties. The solution to Maxwell’s equations was verified accurate and then coupled computations with propellant plasma were conducted. These coupled computations showed good order of magnitude accuracy with a simple onedimensional model however failed when the plasma began to accelerate due to the Lorentz force. The electric field, magnetic field, current density, and Lorentz force were all aligned in the proper vector directions. The computational failure occurred due to rapid, fictitious increases in the induced electric field in the vacuum created between the accelerating plasma and drive coil. Possible solutions to this problem are to decrease the time step and refine the grid density. Although complete acceleration of propellant plasma has yet to be computationally computed, this study has shown successful coupled computations with Maxwell and Navier-Stokes equations for a pulsed inductive plasma accelerator.