In the present work, the collapse of a single non-spherical gas bubble situated above a rigid wall and surrounded by a viscoelastic liquid is studied numerically using the boundary element method (BEM). Assuming that the liquid obeys the “material” Maxwell model as its constitutive equation, the modified viscous potential theory developed by Lind and Phillips³²⁾ is used to investigate the role played by the buoyancy and Bjerkness forces on the bubble collapse. To simplify the analysis, the bubble is assumed to retain its axisymmetric shape during its collapse. Also, the non-condensible perfect gas inside the bubble is assumed to undergo an adiabatic process during the bubble's collapse. The numerical results show that at the latest stages of the collapse, an oscillating liquid jet is developed if the Bjerknes and buoyancy forces are more dominant than the viscous and elastic forces. However, if viscous and elastic effects are more dominant, there will be no liquid jet formed near the wall with the bubble preserving its nearly spherical shape all throughout its oscillatory motions.