The phenomenon of stretched cells in the vicinity of an oscillating bubble is investigated in this work. Experiments reveal that a red blood cell can be stretched up to five times its initial size towards the end of the collapse of a laser-induced cavitation bubble. We hypothesize that the cell elasticity is crucial for the elongation. In order to get insight in the physics involved, numerical simulations based on potential flow theory (with the boundary element method) are performed. A simple membrane tension model for the elongating cell is employed. We observe that the stretching can only occur if the cell exhibits some elastic properties within a certain threshold. The maximum elongation occurs when the oscillations of the bubble and cell are out of phase, that is, the bubble oscillates at half the oscillation time of the cell.