This paper presents the induced mathematical modeling equations for evaluating the operation stability with automatic transmission of heavy duty vehicle. This theoretical approach indicates that linearized governing equations of system can be converted into eigen-value problems. if the eigen-value has positive number, we can predict the engine operating point locates an unstable operating region. To be a stable state, the unstable operating point diverges toward a stable point which is able to maintain uniform velocity. Based on the previous theoretical analysis, we carry out dynamic simulation to show the behavior of engine operating point and torque converter in transient state. As a result of the dynamic simulation, the suggested theoretical method is found to be reasonable for evaluating the operation stability of a torque converter. In addition, the numerical results explain the engine stops and fluctuating phenomenon in reality.