Understanding the mechanisms behind the cavitation erosion resistance of elastic materials is the basis for the development of new cavitation erosion resistance materials. This paper employs underwater low-voltage discharge to induce cavitation bubble, combined with high-speed photography, shadowgraph methods, and transient pressure measurement systems to experimentally investigate the evolution and intensity of shockwave from bubble collapse near elastic-rigid composite boundary. Under the condition of constant elastic material thickness, with the bubble–wall distance increasing, shockwave shape evolves from multi-layers to single-layer. The peak pressure of the shockwave shows a trend of decreasing, then increasing, and finally stabilizing with increase in the bubble–wall distance. Furthermore, it was found that the elastic-rigid composite boundary causes the shockwave to reflect twice. As the material thickness increases, the intensity of the first reflected shockwave from the elastic surface decreases initially, then increases, and eventually stabilizes. However, that of the second reflected shockwave decreases. The total energy of the two reflections at the elastic interface is less than 4% of the mechanical energy of the bubble at its maximum volume. Finally, after the energy dissipation by the two reflections and material deformation, the elastic layer substrate withstands over 70% of the total mechanical energy of the cavitation bubble. There is an optimal elastic material thickness to minimize the shockwave load on the elastic layer substrate under the condition that the elastic-rigid composite boundary does not affect the evolution of cavitation bubble shape. These findings are significant for understanding bubble dynamics near elastic-rigid composite boundaries and provide theoretical support for developing cavitation erosion-resistant materials in engineering.