Electrical discharge machining (EDM) is a nonconventional machining process that involves the formation of a plasma in an interelectrode gap filled with a dielectric that melts and vaporizes the electrodes (tool and workpiece) when a voltage is applied across them. This work models the plasma discharge in the EDM process to describe plasma characteristics such as electron density, heavy species densities, plasma potential, and plasma temperature using chemical kinetics, fluid flow, and heat transfer mechanisms in a 1D domain in the direction of the gap. The 1D domain allows the model to utilize surface reactions on the electrode walls necessary for sustaining the plasma reactions. The domain also provides a perspective of the plasma characteristics near the workpiece. Temperature results are compared with the experimental data obtained from spectrometer measurements. Additionally, an estimate of the plasma diameter is made and compared with actual high-speed camera images. The effect of EDM parameters such as supply voltage and interelectrode gap size on plasma characteristics is studied. The model predicts the incumbent heat flux on the workpiece electrode for small gaps which could have applications in the development of melt-pool models of EDM. Finally, the model provides a physics-based understanding of the mechanisms of plasma generation in the EDM process.