Wrap each glass vial in bubble wrap. Bubble wrap offers the best initial layer of protection. Newspapers do not offer protection for glass. Bubble wrap envelopes glass in packets of air, supplying adequate cushion.
Select a box that will fit your vials snugly but not too snugly; if the box is too small, your vials can break easily upon impact. If the box is too big, though, the vials can fall when shifted and break.
Place packing peanuts on the bottom of the box.
Place your bubble-wrapped glass vials in the box. Place more packing peanuts over the vials, so that your box is packed so tightly that your vials cannot move around.
Put the lid on the box or tape it shut, according to whether you're using a Tupperware container or cardboard box.
Indicate fragile on your box if you're intending to ship it. Write the word "Fragile" on each and every side of the box, preferably in large red letters with a permanent marker. Inform the post office employee that your package is fragile so that he or she can stamp it and offer insurance in case it breaks.