A numerical model for the radio-frequency (RF) ion thruster discharge chamber is developed to simulate the inductively coupled plasma. To simulate real life applications, a transformer model formulation is incorporated with fluid and electromagnetic models. The discharge chamber is assumed to be axially symmetric. Euler equations are modified to include the Lorentz force and forces due to collisions to represent the motion of the plasma. The plasma is treated as a compressible gas. Plasma generation due to ionization is added to the continuity equation. Magnetic vector potential equation is solved for the electromagnetic fields. Spatial distribution of the plasma parameters is obtained. Plasma is assumed as the secondary of an air-core transformer to represent the matching circuit. The resulting model is a tool to be used in thruster performance evaluation.