variavel0=GUSTAVO COELHO ABADE - gcabade@ig.com.br UNB FRANCISCO RICARDO DA CUNHA - frcunha@unb.br UNB Abstract. The work investigates suspension of equal and unequal particles sendimenting in a box with periodic sides. Computer simulations of sedimentation velocity and its variance based on statistics over a large number of random configurations are calculated for monodisperse and bidisperse suspensions. The simulations indicate that the variations in the individual particles velocities are due to varying configurations of neighbouring particles and the result of viscous hydrodynamic interactions. It is shown how the sedimentation velocity and its variance might depend on the size of a system with a periodic boundary conditions. It is also explored the effect of polydispesity and particle concentration on the velocity flutuations. From dynamic simulations velocity auto-correlation functions and hydrodynamic diffusivities were obtained. The results for the mean setting velocity were found to be in agreement with theory and experiments. The results for the hydrodynamic diffusivities show strong vertical-horizontal anisotropy. Keywords. random suspensions, sedimentation, particle interactions, velocity fluctuations.