The method of the invention, where the bumper (10) includes a bumper armature (14) and the structure (22) includes an understructure (22) comprising a cross beam (26), rails (24) and fastening brackets (28) carried by the rails (24), comprises positioning and securing the armature (14) onto the structure (12) relative to predetermined geometrical references, some of which are connected to the fastening brackets (28) while others are connected to the beam (26). More precisely, a first portion (16) of the armature (14) is fitted with compensation parts (20) adjustably mounted on the armature (14), a second portion (18) of the armature (14) is attached on the fastening brackets (28), the position of the compensation parts (20) being such that they are spaced from the beam (26) when said attachment is done; the placing of the armature (14) onto the structure (12) is completed by moving the compensation parts (20) so as to bring them in contact with the beam (26).