Rinse off the plums in cool running water. Dry them with a paper towel.
Place the plums in a paper bag. Roll the open ends of the bag together loosely to shut it and then leave the bag on a table or shelf in a cool room.
Check the plums every day for ripeness. Plums usually soften near the stem area first as they ripen. A ripe plum will indent with only gentle pressure from your finger. The skin of a ripe plum develops a faint powdery hue.
Refrigerate ripe plums, placing them in an open plastic bag in the crisper section of your refrigerator. Ripe plums may keep for two to four weeks when refrigerated.