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However, it does not model the shallow part of the fault of the ruptured area because Dalguer <i>et al</i>. (2001) showed by the dynamic fault rupturing simulations that the fault rupturing reaches the ground surface as fault dislocations after the rupturing of the basement rock, which radiates seismic energy, propagates in the sedimentary rock from the depth of a few kilometers to the ground surface even if the sedimentary rock has little or no stress drop. Hence, the ‘Recipe’ can not predict permanent displacements in the area very close to the fault trace. </p><p>　On the other hand, the 2016 Kumamoto, Japan, earthquake provided precious data of strong motions including the permanent displacements, and these permanent displacements caused severe damage to structures. Since then, several research teams have conducted studies to reproduce and predict these strong motions including permanent displacements. </p><p>　I reviewed these studies, categorizing them into three groups: reproducing strong motions by kinematic source model, extending the ‘Recipe’ in order to model the shallow part of the ruptured area, and reproducing permanent displacement by empirical model. I finally proposed two procedures for modeling the second- and third-stage earthquakes, which have surface fault breakings such as the Kumamoto earthquake, to predict strong motions including permanent displacements in the areas very close to the fault trace on the ground surface. 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