For underwater supercavitation vehicles powered by jet propulsion, the stability and morphological control for ventilated cavity are the key issues. In this paper, we use the VOF coupled level set interface tracking method, the compressibility of the gas is considered. By changing jet strength and model length, a series of numerical simulations is studied on the interaction between ventailated cavity and supersonic tail jets, and focused on the stability and closed position of the cavity. The numerical results show that:1. Under the action of the supersonic tail jet, the interface of the ventilated cavity will experience expansion, necking, fracture and retraction, and then begin to periodically oscillate and deflate. The morphological length of the ventilated cavity is greatly reduced compared with that under the condition of no jet. 2. Strong shear on both sides of the gas-liquid interface may induce cavity instability and collapse, and this cavity instability mechanism mainly depends on two dimensionless parameters (the ratio of jet thrust and cavitator resistance) and (The ratio of the model length to the diameter of the cavitator). The larger and the smaller , the more easily the cavity is destabilized. On this basis, the critical curves for the two states of stability and instability in the calculation examples are further summarized. 3. The more stable the cavity, the lower the amplitude and frequency of the pressure fluctuation at the nozzle outlet. At this time, the ventilated cavity could provide stable ambience for the rocket engine. 4. For the condition of instability cavity, the cavity is closed at the nozzle outlet; while for the stable cavity, the length from the nozzle outlet to the closed position is only related to the parameter , but not to the model length.