Abstract: A system of warehouse racks placed perpendicularly to a working aisle. After selecting a place of storage of a given product, at least one rack is moved to the working aisle. The goods are placed or removed from the indicated place in the rack, and then the rack is moved to an initial position. The movement of the rack to the working aisle and its return to its initial position is made by movable, shared platform moving under at least one row of racks that is perpendicular to the direction of movement of the rack and parallel to the working aisle. The system includes a drive system, a power supply system, at least one running gear, a rack lifting system and a positioning system extending or retracting the rack. During movement to the working aisle and return to the initial position, the rack is lifted above the ground surface by the positioning system of the shared platform.