This paper presents a monolithic method for modeling of fluid-structure interaction problems involved in geohazards encountering with countermeasures using material point method (MPM). The basic concept of MPM is introduced firstly, and then the constitutive models used in geohazards-structure interaction problems, including elastic model, Drucker-Prager elastoplastic model, Newtonian fluid and Bingham fluid model and their implementations in coupling with MPM are presented. Three benchmark problems, including dam break of water column and impact on elastic obstacle, dry granular sand impact on rigid structure, and viscous debris flows flowing down a drainage chute with and without oblique symmetrical sills, are examined. Comparison of the results with those of the laboratory tests has verified the reliability of MPM approach on the fluid-structure interaction problems involved in geohazards.