Numerical calculations of the propagation properties of density pulses through an ion‐beam plasma system are presented. Both stable and unstable situations are investigated. The calculations are based on the linearized Vlasov equation, which is solved as an initial value problem. Solutions are presented both for pure velocity modulation and for pure density modulation of the beam. The propagation properties are found to be strongly dependent on the modulation form. In the case of velocity modulation the perturbation grows even under stable conditions, while in the case of density modulation only an instability causes growth.