To reproduce realistic characteristics of ice sheets (i.e., velocities, thicknesses and extensions of Greenland and Antarctica), large scale ice sheets models have to empirically correct the rheological law of ice derived from laboratory measurements on isotropic samples. The modication usually consists in introducing an ad hoc enhancement factor in the Glen’s flow law. For grounded ice, most authors found that an enhancement factor ranging between 3 and 5 gives adequate results and is further justified by the strong anisotropic behavior of polycristalline ice in simple shear. In other words this means that grounded ice in the model must be 3 to 5 times softer than predicted by the Glen’s flow law. However, to simulate the entire Antarctic ice-sheet, ice-shelves must also be considered and in that case the enhancement factor must be smaller than one to prevent unrealistic high velocities. Although these two different behaviors (soft grounded ice / stiff ice-shelf ice) are empirically taken into account in ice-sheet models, no founded proof has never been proposed to explain this rheological difference between ice-sheet and ice-shelf. Here, using an anisotropic ice flow model, we show that the two different values of the enhancement factor needed for grounded and floating ice can be quantitatively explained by the anisotropic behavior of polar ice and the difference of stress regime between the grounded and floating parts.