An algorithm for a computer simulation of the dynamics of a hard sphere suspension without hydrodynamic interactions is presented. This is an extension of the Monte Carlo method for hard spheres which makes it possible to calculate dynamical quantities of the system. Since these quantities are quite sensitive to the time interval Δt corresponding to one simulation step per particle, an extrapolation procedure for the limit Δt→0 is proposed. Simulation data for the mean square displacement are presented for various volume fractions between 0.1 and 0.5. It is shown that the temporal behaviour of the time derivative of the mean square displacement is very well described by the stretched exponential function exp(−const. ×√t).