Abstract: A packing case for a plunger or a piston rod of a reciprocating machine comprises packing cups, each packing cup comprising a body with a hole for the passage of the plunger or rod and a sealing ring seat for housing a sealing ring which slidably bear against the plunger or rod. Packing cups are aligned with each other in series. The packing case comprises lube oil ducts for supplying lube oil from an end of the packing case to the sealing ring seat. Each packing cup comprises sectors, each sector comprising at least lube oil duct portions. The packing cups are positionable to bring, one sector at a time in an activation position where some of the lube oil duct portions of the sector are connected with the lube oil duct portions of an adjacent packing cup to form lube oil ducts. The packing cups are lockable.