A machine (M) for filling and capping vials (F), comprising, arranged in a cascade fashion: a supply station (1) of empty vials (F); an Archimedes screw (2) having a rotation axis parallel to a longitudinal development of the machine (M), supplied with the vials (F) in arrival from the supply station (1); a device (D) for disengaging a predetermined number of vials (F) from the screw (2), activated in phase relation with the screw (2), and for transferring the vials (F) transversally; a comb conveyor (3), step-moved and designed to receive the predetermined number of vials (F) from the device (D); a filling station (6, 7), designed for introduction of a liquid solution contemporaneously into a plurality of vials (F); a capping station (10, 11) for contemporaneously sealing a plurality of vials (F); an outlet zone (U) for conveying the vials (F) out of the operating line of the machine.