Theory and applications of continuum damage mechanics for ice are discussed, and on this basis, an ice damage model, valid at low stresses, is proposed. The model describes the damage itself, the rheology of the damaged ice, and the damage evolution. A local damaging and healing law is considered, and its parameterization is motivated. The model parameters are inferred from published data of laboratory experiments. The model is subsequently implemented in a finite element code and applied to the prediction of a calving process and to the destabilization of an ice chunk from a hanging glacier. Numerical results show good agreement with field measurements.