The invention relates to a process for producing and assembling an aseptic container (100, 200) suitable for containing and supplying medical liquids comprising in sequence at least the steps of extruding a plastic material, operating on the intermediate tubular element obtained by blow moulding so as to obtain at least a hollow body (2, 202) and sealing the hollow body (2, 202) with a cap having a small size or applying an insert, comprising at least a portion (4, 204) with facilitated breakage.