The thesis considers battle termination a unit reaching its so-called breakpoint in ground combat as a rational decision process. A commanders decision to break contact with an enemy force and withdraw from the battlefield is analyzed for company-size infantry units. Two approaches to terminate an engagement are presented. The first approach is based on extrapolation of observations on past battle history into the future with no assumption about combat dynamics. The second is based on the assumption of known Lanchaster-type combat dynamics possible with unknown parameters to be estimated and uses Kalman filtering. Possible applications of such models are discussed, and related areas for future study are recommended.