The development of gas turbine needs to studying and development each of its components. In this paper we will focus on the study of the compressor used in gas turbines. So we can study it we will be using mathematical modeling, which aims to find a mathematical description of the system studied and study the dynamic behavior of it in order to improve his performance, and use mathematical modeling to save time and cost at the improvement and development of products or in the case of the creation of new products through simulation that enrich us all costly and timeconsuming testing stations. Also it helps us to clarify the physical phenomena or unwanted effects and enable us to determine the full parameters required in accurate design.