Abstract: Lanchester equations and their extensions are widely used to calculate attrition rates in combat modelling. This paper examines how Lanchester models fit detailed daily data on the Battle of Kursk using the technique of Maximum Likelihood Estimation (MLE). A detailed database of the Battle of Kursk of World War II has been developed recently. In past several studies have been carried out on the Kursk data. Although different forms of Lanchester Models have been applied for fitting these data, little efforts have been made to apply the MLE technique. The previous studies are mostly based on the least-square methods of parameter estimation and have a number of drawbacks. First, these estimators do not possess optimality properties such as consistency, sufficiency, and efficiency. Second, since these approaches do not consider the statistical properties of the parameters, and therefore statistical inferences from these approaches cannot be drawn. This paper compares the results of the MLE with the results of estimation techniques studied in the past. Various goodness-of-fit measures have been proposed for the accuracy assessment of the MLE to that of the previous approaches. The results show that the MLE is statistically more accurate than existing approaches.