The 8th October 2005 Kashmir Earthquake Mw 7.6 involved primarily thrust motion on a NE-dipping fault. Sub-pixel correlation of ENVISAT SAR images gives the location of the 80 km-long fault trace (within 300--800 m) and a 3D surface displacement field with a sub-metric accuracy covering the whole epicentral area. The slip distribution inverted using elastic dislocation models indicates that slip occurs mainly in the upper 10 km, between the cities of Muzaffarabad and Balakot. The rupture reached the surface in several places. In the hanging wall, horizontal motions show rotation from pure thrust to oblique right-lateral motion that are not observed in the footwall. A segmentation of the fault near Muzaffarabad is also suggested. North of the city of Balakot, slip decreases dramatically, but a diffuse zone of mainly vertical surface displacements, which could be post-seismic, exists further north, where most of the aftershocks occur, aligned along the NW-SE Indus-Kohistan Seismic Zone.