Detailed rupture process of the 2001 Geiyo, Japan, earthquake (Mw = 6.8), which is a slab earthquake in the Philippine Sea slab, is investigated from the inversion of strong motion waveforms. In the inversion, a realistic curved fault model is assumed, and the one-dimensional underground structure models considering the deep slab structure and the shallow surface layers are used. The estimated seismic moment and the maximum slip are 2.1 ¿ 1019 N m and 2.4 m, respectively. The total rupture duration is ~10 s. The obtained rupture process is very complex. The rupture changed gradually from a normal fault type into a more strike-slip type during its propagation. The slip distribution is heterogeneous, and the rupture area extends over both of the slab oceanic crust and the slab oceanic mantle. In the medium of the source area, there exists a large velocity contrast at the slab oceanic crust-mantle boundary. The largest slip is seen in the low-velocity (low-rigidity) oceanic crust. It is reasonable from the viewpoint of rupture dynamics that large slip occurs in the low-rigidity layer, which is easier to deform. Thus the obtained slip model suggests that the rupture process of the 2001 Geiyo earthquake was strongly influenced by the heterogeneity of the background medium.