Gas turbines are one of the most important internal combustion engines in the modern world's transportation. Any possible improvements of the performance of the gas turbine engines would help to minimize the world's annual fossil fuel consumption and hence the emissions of the adverse greenhouse gases. Therefore, modelling and simulation of gas turbines have been a major focus of many fields in aviation to improve their performance. In this work, it is aimed to model a turbojet gas turbine engine theoretically and computationally. On this basis, the pre-established equations were implemented in MATLAB Simulink to create a model of a turbojet engine. The influence of atmospheric conditions was also taken into account in creating the model. Furthermore, GasTurb was used to study the turbojet engines and provided useful results to explore the engine performance. The theoretical and Simulink models were in a good agreement within reasonable limits which verifies the correctness of the Simulink model established in this paper. Therefore, the proposed model can be used in investigating the performance of various types of turbojet engines without performing time taking theoretical calculations.