A two-dimensional model is developed to simulate discharge of a lithium/thionyl chloride primary battery. As in earlier one-dimensional models, the model accounts for transport of species and charge, and electrode porosity variations and electrolyte flow induced by the volume reduction caused by electrochemical reactions. Numerical simulations are performed using a finite volume method of computational fluid dynamics. The predicted discharge curves for various temperatures show good agreement with published experimental data, and are essentially identical to results published for one-dimensional models. The detailed two-dimensional flow simulations show that the electrolyte is replenished from the cell head space predominantly through the separator into the front of the cathode during most parts of the discharge, especially for higher cell temperatures.