This invention relates to a maintaining device for mechanical pieces, comprising a slider-holder formed by a body and a head with a central bore in which a part of the piece to be maintained is placed, the piece to be maintained exceeding the head, the head comprising a conical area, the maintaining device having at least two sliders and an actuation element for the sliders, wherein the head comprises at least two lateral bores, one leading into the conical area and the other to the central bore, the sliders are placed in the lateral bores, the sliders being adjustable in the lateral bores, the sliders exceeding the conical area of the head, the actuation element of the sliders being arranged to move the sliders in the corresponding lateral bores along an axis perpendicular to a longitudinal axis of the central bore.