Interface instability of droplet and formation of the liquid jet caused by internal volume oscillation are directly related to liquid pumping and mixing of microfluidic devices. Complex morphology jet enables liquid shaping, which is advantageous for industrial applications and biomedical engineering. In this study, the interface instability of cylindrical droplet between plates is investigated. The problem is analyzed through numerical simulation and experimentation. In the experiment, a single-pulse laser is used to generate cavitation at the center of the cylindrical droplet between two polymethyl methacrylate plates, and the physical progress is captured by high-speed photography. A compressible two-phase solver in the open source code OpenFOAM is used to simulate the 3D progress of bubble pulsation and droplet jet in consideration of viscosity and surface tension. Numerical methods adopt large eddy simulation. Results show that the interface density gradient is not collinear with the pressure gradient due to the shock wave impact and the bubble pulsation, that is, the baroclinic effect is the main cause of the instability at the droplet interface. The mechanism of the radial jet formation in the first period of bubble pulsation is closely related to the interface instability. A pair of vortex rings is formed under the influence of instability, thereby causing a stacking phenomenon on the jet head and eventually being cut. Affecting factors of the instability of the droplet interface are discussed. A high instability intensity of the droplet interface can be caused by a large initial bubble energy and a small contact angle. The instability strength of the droplet interface and the mode of jet formation are very sensitive to the curvature of the initial droplet shape. Relevant results may provide a reference for further understanding of interface instability and related engineering applications.