This study aims to model anisotropic damage (i.e. increase of porosity and loss of stiffness) and healing (i.e. recovery of stiffness) in salt rock subject to microcrack initiation, propagation, and rebonding. We introduce enriched fabric tensors in a Continuum Damage Mechanics model to link micro-crack evolution with macroscopic deformation rates. We carry out creep tests on granular salt assemblies to infer the form of fabric descriptors. We use moments of probability of fabric descriptors to find relationships between microstructural and phenomenological variables. Creep processes in salt include glide, cross-slip, diffusion, and dynamic recrystallization. We assume that healing is predominantly governed by diffusive mass transfer. We model the corresponding crack cusp propagation on grain faces by means of a two-dimensional diffusion equation. We calibrate this grain-scale healing model against experimental measures of crack cusp propagation distance. We simulate the opening, closure and rebonding of three orthogonal families of micro-cracks during a compression-tension loading cycle. Multi-scale model predictions illustrate the evolution of stiffness, deformation, and crack geometry during the anisotropic damage and healing process, and highlight the increased healing efficiency with time. We expect that the proposed modeling approach will provide more precise and reliable performance assessments on geological storage facilities in salt rock.