Abstract.Charging of individual dust particles in contact with hot plasmas is studied by numerical methods. The dust particle is treated as a rigid solid body, composed by either perfectly insulating or conducting material. The collisionless plasma, consisting of electrons and singly charged ions, is simulated by Particle-in-Cell methods in two spatial dimensions. It is demonstrated that the surface conditions, i.e. roughness, of the dust particles are significant for the charging. In a streaming plasma, a dust grain develops an electric dipole moment which varies systematically with the relative plasma flow. The strength and direction of this dipole moment depends critically on the material. We observe also Langmuir oscillations excited in the vicinity of the particles, and analyze the spatial variation of their spectral distribution.