The article focuses on the explanation of the basic principles and functions of harmonic gear systems. The main objective of the article is to comprehensively explain the relations concerning the main construction parameters of these special gear systems and their impact on the backlash. It also includes basic mathematical relationships between the reaction elements, mechanical characteristics, cogging types and the properties of the harmonic gear systems. This article focuses mainly on the preparation of the finite element 3D computational model of the harmonic drive gear and tooth backlash analysis. The results of the simulation were analysed in the final part of the article.