The paper deals with a single-spool single-jet turbo engine with variable area exhaust nozzle for aircraft use. Based on engine’s non-linear motion equations, its mathematical model was established; a new form of the model was issued, by using the finite differences method to bring it to a linear form, which was brought to a dimensionless form after convenient equations’ processing and then the Laplace transformation was applied. The final form of the model was determined by a matrix description and using an algebraic solving method; two equations, concerning the main outputs, were selected and studied. Two essential coefficients (engine’s time constant and stability constant) were identified and their variations inside the range of engine’s rotational speed and flight altitude were studied. Engine’s quality was estimated performing engine’s step response studies. Some conclusions regarding engine’s stability and its idle speed establishing was also presented.