Summary: A numerical simulation has been carried out to study the interaction of a cavitation bubble and an elastic membrane. Boundary element method is used to simulate the physics of the membrane between two fluids which are assumed to be same (water) for simplicity. The intent of this paper is to clearly investigate the bubble-membrane interaction. Elasticity of the membrane plays an important role on the behavior of the bubble. For example, a bubble near a ’stiff’ membrane (high elasticity), jets toward it (the same as the rigid boundary). The influence of two main parameters, namely, dimensionless distance of the bubble center to the membrane initial position \((H')\) and the dimensionless elasticity of the membrane \((E')\) are discussed. We have considered the dimensionless distance of the bubble center to the membrane initial position in the range of \(0.5\leqslant H'\leqslant 1\) and a membrane of dimensionless elasticity in the range of \(0.01 \leqslant E'\leqslant 10\). An increase in \(H'\) leads to a decrease in the membrane displacement from its initial position. Also, increasing of \(E'\) leads to a change in the behavior of the bubble from spherical collapse to jetting toward the membrane (in a same \(H'\)) and decreasing in membrane displacement.