The gas turbine engine is a complex assembly of a variety of components that are designed on the basis of aerothermodynamic laws. The design and operation theories of these individual components are complicated. The complexity of aerothermodynamic analysis makes it impossible to mathematically solve the optimization equations involved in various gas turbine cycles. When gas turbine engines were designed during the last century, the need to evaluate the engines performance at both design point and off design conditions became apparent. Manufacturers and designers of gas turbine engines became aware that some tools were needed to predict the performance of gas turbine engines especially at off design conditions where its performance was significantly affected by the load and the operating conditions. Also it was expected that these tools would help in predicting the performance of individual components, such as compressors, turbines, combustion chambers, etc. At the early stage of gas turbine developments, experimental tests of prototypes of either the whole engine or its main components were the only method available to determine the performance of either the engine or of the components. However, this procedure was not only costly, but also time consuming. Therefore, mathematical modelling using computational techniques were considered to be the most economical solution. The first part of this paper presents a discussion about the gas turbine modeling approach. The second part includes the gas turbine component matching between the compressor and the turbine which can be met by superimposing the turbine performance characteristics on the compressor performance characteristics with suitable transformation of the coordinates. The last part includes the gas turbine computer simulation program and its philosophy. The computer program presented in the current work basically satisfies the matching conditions analytically between the various gas turbine components to produce the equilibrium running line. The computer program used to determine the following: the operating range (envelope) and running line of the matched components, the proximity of the operating points to the compressor surge line, and the proximity of the operating points at the allowable maximum turbine inlet temperature. Most importantly, it can be concluded from the output whether the gas turbine engine is operating in a region of adequate compressor and turbine efficiency. Matching technique proposed in the current work used to develop a computer simulation program, which can be served as a valuable tool for investigating the performance of the gas turbine at off-design conditions. Also, this investigation can help in designing an efficient control system for the gas turbine engine of a particular application including being a part of power generation plant.