A holding device for a rim of a vehicle wheel, comprising: a base plate having a central through hole for sliding onto a shaft of a balancing machine, a plurality of retaining elements, each of the plurality of retaining elements rotatably mounted on the base plate, a synchronization element for synchronizing the rotation of the plurality of retaining elements, the synchronization element rotatably provided on the base plate, and a locking element for locking a rotational position of at least one of the plurality of retaining elements or the synchronization element, wherein the plurality of retaining elements and the synchronization element each comprise a coupling portion (15, 35) for form-fitting coupling of the rotational movement of the plurality of retaining elements and the synchronization element, each of the plurality of retaining elements comprising: a base portion having a central mounting portion for mounting the retaining element on the base plate and for defining a rotation axis of the retaining element, and a retaining portion mounted on the base portion for engaging with the rim of the vehicle wheel, wherein for each of the plurality of retaining elements, the coupling portion is provided concentrically with the central mounting portion to the outer circumferential side of the base portion, wherein each of the plurality of retaining elements further comprises an elastic coupling portion biasing the coupling portion of the respective retaining element towards the coupling portion of the synchronization element for ensuring the form-fitting coupling of the synchronization element and the plurality of retaining elements, characterized in that for each of the plurality of retaining elements, the base portion has an outer peripheral diameter smaller than an inner peripheral diameter of the coupling portion so as to form a gap between the base portion and the coupling portion, wherein the elastic coupling portion is provided in the gap between the base portion and the coupling portion for elastically coupling the base portion and the coupling portion. a base plate having a central through hole for sliding onto a shaft of a balancing machine, a plurality of retaining elements, each of the plurality of retaining elements rotatably mounted on the base plate, a synchronization element for synchronizing the rotation of the plurality of retaining elements, the synchronization element rotatably provided on the base plate, and a locking element for locking a rotational position of at least one of the plurality of retaining elements or the synchronization element, wherein the plurality of retaining elements and the synchronization element each comprise a coupling portion (15, 35) for form-fitting coupling of the rotational movement of the plurality of retaining elements and the synchronization element, each of the plurality of retaining elements comprising: a base portion having a central mounting portion for mounting the retaining element on the base plate and for defining a rotation axis of the retaining element, and a retaining portion mounted on the base portion for engaging with the rim of the vehicle wheel, wherein a base portion having a central mounting portion for mounting the retaining element on the base plate and for defining a rotation axis of the retaining element, and a retaining portion mounted on the base portion for engaging with the rim of the vehicle wheel, wherein for each of the plurality of retaining elements, the coupling portion is provided concentrically with the central mounting portion to the outer circumferential side of the base portion, wherein each of the plurality of retaining elements further comprises an elastic coupling portion biasing the coupling portion of the respective retaining element towards the coupling portion of the synchronization element for ensuring the form-fitting coupling of the synchronization element and the plurality of retaining elements, characterized in that for each of the plurality of retaining elements, the base portion has an outer peripheral diameter smaller than an inner peripheral diameter of the coupling portion so as to form a gap between the base portion and the coupling portion, wherein the elastic coupling portion is provided in the gap between the base portion and the coupling portion for elastically coupling the base portion and the coupling portion.