In this research, the collapse of a spherical caviation bubble contained in a large body of upper con-vected Maxwell fluid was studied theoretically. A fully explicit numerical scheme was developed which could track the bubble surface without iteration. It was observed that, when Re was less than 10, fluid elasticity accelerated the collapse in the early stage of collapse while in the later stage it rearded. When Re was larger than 10, however, fluid elasticity was no longer effective in changing the pace of collapse due to the large inertia. The retardation for Re<10 was expected to be related with the reduced cavitation damage in viscoelastic fluids.