The elastic fixing for a piston (2) of a variable compression ratio engine (10) includes at least one metal rod (15) kept under tension between the piston (2) and the transmission member (3) and which applies a strong contact pressure between the base of the piston (2) and the top face of the transmission member (3), the piston (2) being tightened according to a previously calculated angle enabling the metal rod (15) consisting of a stud (16) to be subjected to a desired tension force and the tightening prestress to be reached between the piston (2) and the transmission member (3), and indexed in rotation relative to the transmission member (3), by an additional tightening which does not significantly increase the tightening pre-stress, the stud (16) continuing to elongate with the same tension force by plastic deformation.