Shock absorbing structure (10, 10") for a vehicle comprising a side sill (2) comprising two chassis frame side members (4, 4") which together support a bumper beam (6, 6"), said shock absorbing structure comprising said bumper beam and an absorber (7, 7") interposed between each chassis frame side member and said bumper beam, said absorber having a working part (71) intended to deform in the event of an impact under the effect of a load below the limit load beyond which said chassis frame side member undergoes plastic deformation, said absorber being a section piece of which one end (72) is inserted inside the open end (5, 5") of said chassis frame side member and fixed thereto, characterized in that said absorber is an extruded aluminium alloy section piece of which the part not inserted inside said chassis frame side member or inside said bumper beam, which corresponds to said working part, has a length greater than 5 times its radius of gyration defined by formula (I), where I is the quadratic moment and S the cross-sectional area of said section piece, said cross section being such that, under the effect of a substantially frontal impact, said working part is able to deform in crumpling over a length such that the longitudinal crush distance is greater than 4 times said radius of gyration.