AbstractExisting approaches to simulate the bubble growth/collapse in viscoelastic liquids use the integral form of a constitutive equation, that can additionally be analytically integrated over the radial domain. Here we represent the process by a system of simultaneous partial differential equations, with fixed and finite boundaries. This enables a direct computer implementation with commercially available software, with little additional programming effort. The involved co-ordinate transformation preferably does not correspond to the material co-ordinates. The surrounding liquid can be simulated as being a finite film or of infinite extent, with simply a change in one computational parameter. We simulate hydrodynamically induced bubble dynamics in viscolelastic liquids, and estimate the flow strength (elongational strain rate) and its possible role in flow induced scission of polymer chains in liquids experiencing bubble collapse. Calculations are also performed to evaluate the influence of backbone and branch lengths when the surrounding fluid is a branched polymer melt, using the pom-pom model to describe the rheological behavior.