We investigate numerically the elastic interaction between a dipole and an axisymmetrical vortex in inviscid isochoric two-dimensional (2D), as well as in three-dimensional (3D) flows under the quasi-geostrophic (QG) approximation. The dipole is a straight moving Lamb-Chaplygin (L-C) vortex such that the absolute value of either its positive or negative amount of vorticity equals the vorticity of the axisymmetrical vortex. The results for the 2D and 3D cases show that, when the L-C dipole approaches the vortex, their respective potential flows interact, the dipole’s trajectory acquires curvature and the dipole’s vorticity poles separate. In the QG dynamics, the vortices suffer little vertical deformation, being the barotropic effects dominant. At the moment of highest interaction, the negative vorticity pole elongates, simultaneously, the positive vorticity pole evolves towards spherical geometry and the axisymmetrical vortex acquires prolate ellipsoidal geometry in the vertically stretched QG space. Once the L-C dipole moves away from the vortex, its poles close, returning the vortices to their original geometry, and the dipole continues with a straight trajectory but along a direction different from the initial one. The vortices preserve, to a large extent, their amount of vorticity and the resulting interaction may be practically qualified as an elastic interaction. The interaction is sensitive to the initial conditions and, depending on the initial position of the dipole as well as on small changes in the vorticity distribution of the axisymmetrical vortex, inelastic interactions may instead occur.