Numerical results describing the asymmetric collapse of vapor bubbles in an incompressible liquid for various cases of axial symmetry involving boundary conditions which prevent the maintenance of spherical symmetry are presented using a modified Marker-and-Cell (MAC) technique. The effects of fluid viscosity within the body of the liquid are considered, and upon the wall in the wall-proximity problem, but its effects at the bubble wall boundary are neglected. The cases studied include originally stationary spherical bubbles in a pressure gradient, an originally spherical bubble moving through an otherwise stationary liquid at uniform pressure, and an initially spherical bubble in a liquid at uniform pressure close to a rigid wall. This latter case applies approximately also to two identical bubbles collapsing in an infinite fluid in proximity to each other as shown by photographs here included. In all those cases which involve originally spherical bubbles, the bubble collapses in such a way as to form a jet.