Process for manufacturing a plastic hollow body, said process comprising the following steps: a) a molten plastic parison is extruded, in an extruder, through a die; b) at least one longitudinal cut is made in the parison; c) the parison is introduced into a mold comprising two cavities; and d) the hollow body is molded by conforming the parison to the mold cavities, said die being equipped with a passage for the molten plastic which gradually modifies the shape of the parison so that it is substantially flattened on exiting. Die suitable for implementing this process.