Abstract: A linear machine for blow moulding hollow bodies includes: an extruder feeding a head for extruding juxtaposed parisons lying on an imaginary vertical plane parallel to or coincident with the imaginary plane containing the longitudinal axis of the extruder itself; mould and counter-mould assemblies with respective grippers which can be alternately moved along an axis contained in the imaginary vertical plane of the extrusion head itself; and a unit for transferring the containers cyclically formed by the moulds onto a single conveyor located laterally to the path of the mould and counter-mould assemblies. The conveyor resides longitudinally under the extruder. The mould and counter-mould assemblies can move horizontally. Components cyclically and linearly raise and lower the extruder and/or the head, preventing the parison products from interfering both with each other and with the moulds as they come out in a closed condition due to the cooperation with the extrusion head.