A device for packaging and/or applying a cosmetic or care product includes a hollow body forming a housing for the product, a base adapted to support the product and a driving arrangement or means for moving the base in translation so as to vary the volume of the housing. In a disclosed example, the driving arrangement or means includes an actuating member mounted movably in rotation about a shaft and able to be moved along the hollow body that is fixedly attached to the base. The actuating member includes at least one portion forming alternatively a stress surface configured to be put under stress by manual contact and an actuating surface configured to be in engagement along the hollow body.