The efficiency of modeling of the axisymmetric dynamics of a gas bubble near a curved rigid wall by the boundary element method using the fundamental solution of the Laplace equation for an unbounded domain is numerically studied. For this purpose, the problems of the collapse of a bubble near a flat wall and the expansion and subsequent collapse of a bubble near the concave and convex walls are considered. To assess the effectiveness, the results of calculations of these problems are compared with the known results of their calculations using their fundamental solutions for the areas bounded by those walls. The results show the dependence of the numerical solution on the radius of the computational domain on the wall, the number of cells when the domain is uniformly partitioned, and the number of cells when it is non-uniformly partitioned with condensation toward the axis of symmetry along a geometric progression.