An oil rotary vacuum pump of mechanical type (100) is filled with a requested amount of oil at the end of the manufacturing process, then it is stored and then shipped to the user, letting the user to avoid an operation of introducing the proper amount of oil into the pump. The oil leakage is prevented by securing the suction and/or exhaust ports (3, 17) of the pump, which are sealed by means of a removable sealing member, for instance by means of a membrane (21, 23).