Fill a clean bucket or bathtub with water and 1/2 cup to 1 cup of oxygen bleach and mix around.
Add your unfolded, yellowed pillow cases and sheets one at a time.
Let your old yellow pillow cases and sheets soak overnight.
Treat any specific stains on the wet fabric by rubbing in thoroughly a stain treatment.
Wash your pillow cases and sheets alone and using a hot water cycle, unless otherwise specified on the fabric's care instructions. Set your washing machine for a delayed final rinse cycle.
Add 1/2 cup of white vinegar to the wash right before the final rinse cycle.
Hang your sheets and pillow cases to dry outside and in the direct sunlight all day.
Wash your sheets with a commercial whitening agent or a white fabric dye if they are still not white enough. Follow the instructions on the package.