The theoretical and practical application of the Analytic Hierarchy Process (AHP) was covered in the master's thesis. AHP is the most well-known and widely used method of multi-criteria decision-making. The theoretical part of the thesis describes the fundamental principles related to multi-criteria decision-making and the AHP method, providing an overview of ten applications of the AHP method from various scientific articles. This method was used in the first procurement cycle of combat military aircraft in Croatia. Specifically, this example is presented in the practical part of the thesis, in simplified way. In this sense, the real problem is significantly simplified, and we are discussing a simulation of aircraft procurement. Furthermore, actual data is not publicly available. The application of the AHP method was performed using Microsoft Excel software. Data for the simulation were collected with the assistance of mentor, consultation with relevant military personnel, and gathering information from available and open sources. The objective of this master's thesis was to demonstrate the analysis of aircraft procurement and conclude which combat aircraft would be the most suitable for procurement. All steps of the AHP method were implemented.