A floating fish farming plant (1) comprises a cage (6) supported by a buoyant body (2) which is configured for floating in a body of water (W). Lifting means (7) are arranged between the buoyant body and the cage and configured for moving the cage between a position at the level of, or below, the buoyant body and a position in which at least a portion of the cage is above the buoyant body. The cage (6) comprises at least a lower section (6c), forming a bottom portion of the cage, said lower section having a wall comprising an elastic material and/or being elastically connected to the middle section; where by transfer of dynamic forces between the lower section and the adjoining section is reduced. An assembly (18) comprises a plurality of fish farming plants (1).