This article presents a mathematical model of the process of delayed combat operations, in which the actions of two sides are delayed by a certain amount of time, based on the interaction of opposing forces, and defines a methodology for numerical solution. Differential equations with delayed arguments allow a more realistic reflection of the dynamic state of processes related to military operations. The article is to propose a finite difference method for numerically solving initial value problems for a system of linear differential equations under the influence of a constant delay time. The algorithm is based on Euler’s method, and a comparative analysis of the proposed method is provided. The combat operations model is considered as a system of functional differential equations with constant delay. The applicability of the proposed approach is demonstrated using examples of conflicts between two opposing sides.