Irradiation of YBa2Cu3O7-δand Bi2Sr2Ca3Cu3Oxsuperconductors with 300 MeV gold ions leads to the formation of columnar defects along the ion trajectory. These columns consist of amorphized material within the envelope of a displacement-strain field which propagates into the crystal lattice. The morphology of the defects shows a characteristic shape and size depending on the direction of the incident ion with respect to the crystallographic planes of the superconductors. The defects have a circular symmetry for the ion beam directed perpendicular to thea-bplane, while they are larger and elliptical when the beam is parallel to thea-corb-cplanes. A simple model based on the idea of ion-induced localized melting and anisotropic thermal conductivity of these materials helps us to understand the size and shape of these defects.