The ongoing disintegration of large ice shelf parts in Antarctica raise the need for a better understanding of the physical processes that trigger critical crack growth in ice shelves. Finite elements in combination with configurational forces facilitate the analysis of single surface fractures in ice under various boundary conditions and material parameters. The principles of linear elastic fracture mechanics are applied to show the strong influence of different depth dependent functions for the density and the Young’s modulus on the stress intensity factor KI at the crack tip. Ice, for this purpose, is treated as an elastically compressible solid and the conse- quences of this choice in comparison to the predominant in- compressible approaches are discussed. The computed stress intensity factors KI for dry and water filled cracks are com- pared to critical values KIc from measurements that can be found in literature.