The interaction of a laser-induced cavitation bubble with an elastic boundary and its dependence on the distance between bubble and boundary are investigated experimentally. The elastic boundary consists of a transparent polyacrylamide (PAA) gel with 80% water concentration with elastic modulus E = 0.25 MPa. At this E-value, the deformation and rebound of the boundary is very pronounced providing particularly interesting features of bubble dynamics. It is shown by means of high-speed photography with up to 5 million frames s−1 that bubble splitting, formation of liquid jets away from and towards the boundary, and jet-like ejection of the boundary material into the liquid are the main features of this interaction. The maximum liquid jet velocity measured was 960 m s−1. Such high-velocity jets penetrate the elastic boundary even through a water layer of 0.35 mm thickness. The jetting behaviour arises from the interaction between the counteracting forces induced by the rebound of the elastic boundary and the Bjerknes attraction force towards the boundary. General principles of the formation of annular and axial jets are discussed which allow the interpretation of the complex dynamics. The concept of the Kelvin impulse is examined with regard to bubble migration and jet formation. The results are discussed with respect to cavitation erosion, collateral damage in laser surgery, and cavitation-mediated enhancement of pulsed laser ablation of tissue.