An apparatus suitable for both loading and unloading a round body, for example a tire, relative to a stationary shelf comprises, for loading, a body locating member defining a contact surface which confines in fixed location the round body between same and a shelf edge of the stationary shelf and a body lifting arrangement on which the body locating member is movable carried so as to displace the locating member upwardly relative to the shelf edge. For unloading the apparatus comprises an unloading arm defining a body contact surface that is displaceable in movement arranged perpendicular to a rotational axis of the body from a location outside a shelf storage space defined vertically above the shelf where the body is received when on the shelf, to the shelf storage space so as to displace the body off the shelf.