Earthquakes impose great threat to human society because they may cause many geohazards like landslides, debris flow, and sand liquefaction. It is evident that the earthquake-induced large deformation in soils is the primary reason for casualties and severe damage. Therefore, it is worthwhile to investigate mechanisms and characteristics of such large deformation in geotechnical earthquake engineering. Material Point Method (MPM) is a powerful numerical tool for large deformation analysis. In this study, it is improved for seismic analysis, and some simulations of earthquake-induced large deformation are presented. Firstly, we implement transmitting boundary condition and free-field boundary condition [1] in MPM. These boundary conditions enable more accurate seismic loads input and avoid wave reflections at model boundaries. Based on them, the failure process of an elastoplastic slope subjected to seismic loads is modelled, in which the effects of soil properties and role of compressive wave loads are analysed. We further explore the application of hydromechanical MPM, as pore pressure is crucial in some hazards triggered by earthquake, such as sand liquefaction. The saturated two-phase MPM employs explicit u-U formulation [2], and the transmitting boundary is extended to saturated porous media. A bounding surface hypoplasticity model is adopted to model nonlinear soils. Finally, we simulate the response of a building resting on the liquefiable ground under seismic loads to analyse the soil-structure interaction by considering the effect of soil liquefaction and differential settlement.