This article is from the rec.arts.movies.past-films FAQ, by Evelyn C. Leeper evelynleeper@geocities.com with numerous contributions by others.
It is a Jewish custom to place small stones on the graves or tombstones when
one visits them. I have heard at least two explanations for why:
1) It is symbolic of fulfilling the mitzvah (commandment) of helping
to bury the dead. (It also shows that the grave is being
maintained.)
2) It is forbidden to kill any living thing as a memorial to the
dead (this in reaction to pagan practices of the Middle East
during Biblical times) and so flowers are not permitted. Hence
unliving things (i.e., stones) are used instead.
 
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