A numerical method for computing the dynamics of a platelike particle dispersed system is presented. The particle simulation method (PSM) for fiber suspensions is extended to handle a platelike particle, which is modeled with an array of spheres. Each pair of adjacent spheres is connected and deformed by three types of springs; stretch, bend, and twist. The motion of the platelike particles in flow is followed by solving the translational and rotational equations of motion for each constituent sphere. The mobility matrix for each particle is calculated to obtain the hydrodynamic force and torque exerted on each sphere. For the hydrodynamic interaction among particles, the near-field lubrication force is considered when the separation between spheres belonging to different particles is close, but the far-field part is neglected. The method was applied to the dilute and concentrated system. For the dilute system, the motion of isolated square and rectangular platelike particles was calculated in a simple shear flow. The computed rotation orbits of a rigid square platelike particle were in good agreement with those calculated by Jeffery's equation for an oblate spheroid (disk). The characteristic behavior, which is unknown from the classical theory, of the rigid rectangular particle and the soft square particle was revealed. For the concentrated system, transient behavior of the platelike particles in a simple shear flow was calculated by dispersing them into a unit cell with periodic boundaries. The planar orientation of particles was observed in the microstructure of the concentrated system, and furthermore the orientation of the major axis of particles in the shear direction appeared in the rectangular platelike particle dispersed system.