<jats:title>Abstract</jats:title><jats:p>Ice shelves are large floating ice masses, that are formed when glaciers are becoming afloat at the margin of ice sheets. One dominating mass loss mechanism of ice shelves is calving, describing the detachment of icebergs at the front. Ice shelves stabilize inland ice glaciers due to buttressing. If the stabilizing effect of an ice shelf vanishes because of disintegration or thinning, the corresponding glacier accelerates resulting in sea level rise.</jats:p><jats:p>To describe calving and disintegration of ice shelves, it is important to investigate fracture propagation in ice. A powerful method in fracture mechanics is the phase field method which is based on Griffith's theory. It approximates cracks in a diffuse manner by using a continuous scalar field. We propose a phase field fracture model for ice considering its characteristic material properties. The material behavior of ice depends on the considered time scales. On short time scales it behaves like a solid and while it acts like a fluid on long time scales, which classifies it as a viscoelastic material of Maxwell type. This has been verified by observations. The phase field method allows us to simulate typical fracture situations of ice shelves in Antarctica and Greenland.</jats:p>