Combine plums and water in a large Dutch oven; bring to a boil. Reduce heat; cover and simmer 20 to 25 minutes. Remove seeds from plums; return to cooking liquid, and mash slightly. Strain plum mixture through a jelly bag or 4 layers of cheesecloth, reserving 5 cups juice. Discard pulp.
Combine 5 cups juice and sugar in a large Dutch oven; bring to a rolling boil, stirring frequently. Boil until mixture reaches 220° on candy thermometer, stirring frequently. Remove from heat, and skim off foam with a metal spoon.
Quickly pour jelly into hot, sterilized jars, leaving 1/2-inch head space. Cover at once with metal lids, and screw bands tight.