An infusion pump for providing a pressurized liquid flow from a collapsible, deformable reservoir bag includes a magnetically actuated pressurizing member that applies a pressure to the bag in response to the force of magnetic attraction applied by a magnet. In several embodiments, a bag is seated on a platen of magnetizable metal, and a magnet with a compressing surface is mounted for movement toward and away from the platen. As the magnet is moved toward the platen by the force of magnetic attraction, the bag is pressurized between the magnet and the platen. The magnet may be spring biased either toward or away from the platen to alter the relationship between the decreasing volume of the bag and the pressure applied to it, by compensating in a known manner for the change in the magnitude of the magnetic force with the distance between the magnet and the platen. In another embodiment, a pair of magnets are pivotably attached to opposed edges of the platen, so as to be pivotable, "drawbridge" style, toward and away from the platen. In still another embodiment, a fixed magnet attracts a magnetizable metal plate which is connected, by a pivoting linkage, to a pressure plate. A reservoir bag is placed between the pressure plate and a fixed surface. As the metal plate moves toward the magnet, the linkage causes the pressure plate to move toward the fixed surface, pressurizing the bag therebetween.