Apparatus for handling and packaging coils of sheet material, especially steel strip, comprises a rotary capstan with arms that can project through the hollow core of a coil to support the coil. Successive operations of the packaging process are performed at a number of operating stations, at least one of which is so placed that its packaging operation is performed while a coil is so supported. The packaging may comprise an outer sheet metal wrapping applied by rotation of a wrapping arm about the coil to carry the wrapping sheet around the coil circumference. A feed table is provided to align the metal wrapping sheet initially with the coil. Two overlapping wrapping sheets making up a wrapping for a wider coil can be secured together by a welding arm that operates on the sheets as they are wrapped around the coil.