This paper presents a study to describe the behaviour of a non-equilibrium bubble in a fluid (Fluid 1) that is in contact with another fluid (Fluid 2). Fluid 2 is assumed to incorporate some elastic properties, which are modelled through a pressure term at the fluid-fluid interface. The Laplace equation is assumed to be valid in both fluids and the boundary integral method is employed to simulate the dynamics of the bubble and the fluid-fluid interface. Interesting characteristic phenomena concerning bubble oscillations and the deformation of the fluid-fluid interface are studied for a range of parameters (distance from the fluid-fluid interface, density ratios of the two fluids and elastic properties of Fluid 2). Some of the phenomena observed are jet formation in the bubble, bubble splitting, a ring bubble separating from the main bubble, mushroom-shaped bubbles and the dynamic elevation of the elastic interface. Most of these phenomena are only observed when Fluid 2 possesses some elastic properties (besides the usual formation of a high speed liquid jet). Comparisons with experimental observations confirm the validity of our simulations. (c) 2006 Elsevier Ltd. All rights reserved.