The mechanical behavior of glacier ice is governed by its viscoelastic and non-Newtonian properties. It can be described as a Maxwell-type material, exhibiting a short-term elastic and a long-term viscous behavior. Additionally, the flow properties are described by Glen’s flow law, which takes into account the strain-thinning behavior as well as the temperature dependence of the viscosity. To accurately model longer time periods, Glen’s flow law is integrated into a finite deformation framework. The proposed material model is embedded in the phase field method for fracture to model fracture processes in ice shelves. Ice shelves are large floating plates of ice in the ocean that remain connected to the inland ice of a glacier. While they typically float, variations in bathymetry can cause partial grounding in certain areas, known as pinning points. Satellite images show that cracks typically form at these locations. A fully three-dimensional simulation of an ice shelf and its pinning point is carried out, showing good agreement between simulated and observed crack paths.