The multistage axial flow compressor is modeled by the lumped cascade model of interconnected subsystems. Dynamics for each stage of the compressor are established with a state vector which has three state variables of flow rate, pressure and temperature. Compressor characteristics are estimated using the stage stacking method. Lyapunov stability analysis is applied to such a model for each decoupled linear subsystem. A degree of stability is derived from the eigenvalues of symmetric matrices as solutions of the Lyapunov matrix equations. Physically the degree of stability corresponds to the damping coefficient of the Lyapunov function defined at each stage. The degree of stability represents quantitatively the margin between the surge line and the steady state operating lines. The results allow specification of the stage from which the surge will occur when the compressor becomes unstable. The degree of stability is classified into three distribution patterns according to the rotational speed of compressor operation.