Abstract: In a high pressure pump (1) for liquids or gases with a drive unit (2) and a pair of pump units (3) which are connected by a drive element (4) to a drive shaft driven by a motor (6), a considerable simplification in the sense of large scale production with the lowest possible costs is achieved in that each pump unit (3) exhibits its own closed casing, separate from the drive unit (2), the casing has an inlet (8), an outlet (9), and a tight duct through which a portion of a piston, e.g., at least its piston rod, extends, the piston rods of the pump's pistons are connected to one another by a power transmission element (5) of the drive unit (2), and a solid, inherently stable supporting plate is provided, by way of which at least the casings of the pump units (3) and the drive unit (2) are fixed relative to one another.