In this research, the collapse of a spherical bubble contained in a large body of fluid was analyzed theoretically. The governing equations were derived in the Lagrangian frame of reference, and a fully explicit numerical scheme was developed using the Galerkin-finite element method for the upper convected Maxwell fluid of differential model. It was observed that the fluid elasticity accelerated the collapse in the early stage due to the slow growth of viscoelastic stress, while in the laster stage, it retarded the collapse. In the differential model fluid, the pace of bubble collapse was faster than in the integral model fluid, which was ascribed to the effect of rest history. During the collapse bubble rebounds were observed and the rebound period scaled the amplitude.