The numerical simulation and modeling of plasma detachment from a magnetic nozzle is presented. The detachment problem is of key importance to the plasma-based propulsion concepts that employ a guiding magnetic field to control plasma flow and motivated by the needs of the VASIMR (Variable Specific Impulse Magnetoplasma Rocket) project. The detachment of the plasma exhaust is required to produce directed thrust. In the present scenario plasma can stretch the magnetic field lines to infinity, similar to the solar wind. In order to extend the magnetic nozzle model beyond the limitations of analytic theory, a numerical code is developed to simulate steady-state kinetic plasma flows and to evaluate nozzle efficiency. The direct solution of a steady-state problem, as opposed to an initial value problem, eliminates the need to deal with transient phenomena that are of secondary importance for continuously operated plasma thrusters. The new simulation code is verified against the analytic results and then used to model the plasma behaviour for the conditions of the Detachment Demonstration Experiment (DDEX) at the NASA Marshall Propulsion Research Center, Huntsville, Alabama. / text