A finite-element method was employed to analyze axisymmetric unsteady motion of a deformable bubble near the wall. In the present study a deformable bubble in a Newtonian medium near the wall was considered. In solving the governing equations a structured mesh generator was used to describe the collapse of highly deformed bubbles with the Arbitrary Lagrangian Eulerian (ALE) method being employed in order to capture the transient bubble boundary effectively. In order to check the accuracy of the present FE analysis we compared the results of our FE solutions with the result of the collapse of spherical bubbles in a large body of fluid in which solutions can be obtained using a 1D FE analysis. It has been found that 1D and 2D bubble deformations are in good agreement for spherically symmetric problems confirming the validity of the numerical code. Non-spherically symmetric problems were also solved for the collapse of bubble located near a plane solid wall. We have shown that a microjet develops at the bubble boundary away from the wall as already observed experimentally. We have discussed the effect of Reynolds number and distance of the bubble center from the wall on the transient collapse pattern of bubble.