The invention concerns a plant for manufacturing parts made of composite material, in particular sections for an aircraft fuselage, having at least a compaction station in which, in operation, there are provided a mandrel coated of composite material to be compacted and a transport mechanism arranged to transport at least one compaction device on said composite material. The transport mechanism is associated with at least one sling having at least one strip of porous material that, in operation, is in direct contact with the compaction device, and the sling is configured to transport the compaction device onto the composite material through application of a vacuum source at least to the strip of porous material. The invention also concerns a method of and an apparatus for manufacturing parts made of composite material.