A method and installation for processing a mass of pumpable foodstuff material, for example a ground meat mass. The installation comprises a hopper and a positive displacement pump having an inlet and an outlet. A tube structure connects to the outlet of the pump and has a mouth, e.g. leading to a molding device or a sausage machine. A controllable vacuum assembly causes controlled evacuation of air from the mass in the trajectory of the mass from the hopper to a pump chamber. A controllable aeration assembly causes controlled introduction of a gas into the mass at one or more locations in the trajectory of the mass between the pump outlet and the mouth. A gas pressure control device introduces gas into the mass at a controlled pressure that is at least equal to the actual pressure of the mass at the location of introduction of the gas.