Sloshing dynamics of a molten core is one of the fundamental behaviors in core disruptive accidents of a liquid-metal cooled reactor. In addition, solid particle-liquid mixture comprising molten fuel, molten structure, refrozen fuel, solid fuel pellets, etc. could lead to damping of its flowing process in a disrupted core. The objective of the present study is to investigate the applicability of the finite volume particle method (FVP), which is one of the moving particle methods, to 3D motion of liquid sloshing processes measured in a series of experiments. In the first part of this study, a typical sloshing experiment of single liquid phase is simulated to verify the present 3D FVP method for sloshing characteristics that include free surface behaviors. Second, simulations of sloshing problems with solid particles are performed to validate the applicability of the FVP method to the 3D motion of solid particle-liquid mixture flows. Some good agreements between the simulation and its corresponding experiment demonstrate applicability of the present FVP method to 3D fluid dynamics of liquid sloshing flow with solid particles.