In this article, aerodynamic stability of J79 compressor was analytically investigated. For this purpose, conservation equations of mass, momentum and energy were applied with several assumptions .By accomplishment of equations related matrix as well as investigating its eigenvalues, the effect of parameters on aerodynamic stability were assessed. Due to the complexity of the equations used in the matrix, the equations codes in MATLAB and the desired matrix have been provided. By applying the geometry and flow characteristics of J79 engine on the matrix and extract the relevant diagrams, the effect of some parameters on the aerodynamic stability of the engine is evaluated. According to the results, by reducing the mass flow rate through the compressor, the system tends to be working in an unstable condition. By increasing the ratio of upstream to downstream compressor duct length, the aerodynamic stability of the system will increase. Increasing the plenum volume will yield to a considerable reduction in stability. But by increasing the volume of compressor, the system stability will increase. Enhancing the combustion chamber temperature and also increasing the compressor flow area have favorable effects on system stability. The results of this study compared with previous outcome. Significant achievements were observed between both aforementioned results Relatively good alignment between the results has also been observed.