The answer to this question depends on how you define crying. If by crying you mean shedding or producing tears, then the answer is most certainly yes.
Supposedly, all or nearly all mammals that
live on land produce tears to protect and
lubricate their eyes, including you! This is
important because mammals (and you) have eyes that
move in your sockets and your eyes need to stay
moist in order to move properly. Also, the tears help to clean dirt, dust, or any potentially
harmful particles out of your eyes. This is thesame for elephants as it is for you.
If you define crying to mean shedding tears in
response to emotions, then the answer to your
question is a little more difficult. It is easy to
show that elephants produce tears, but it is not possible to demonstrate that these tears result from emotions (what about the elephant's behavior, especially when it is consistent with tears such as the death of a baby), so we cannot really say for sure that elephants cry from emotions.
We think that humans cry in response to
certain emotions, such as sadness, joy,
frustration, or grief. But we do not know this is
true for all humans or just for ourselves. For
humans, we think that tears result from certain
emotions because we have all experienced this
effect directly in our own personal lives.
However, we do not know what emotions elephants
feel, if any, in the same manner that we do not
necessarily know for sure what emotions other
people feel. (What about body language?) This is simply because we cannot measure emotions, (what about: indifferent, moderately angry, angry, enraged, incensed) we can only experience them. As a result, science cannot say whether elephants experience emotions, whether other people experience emotions (what would Sigmund Freud say?), or what these emotions are like. This is because science requires that we be able to measure something (there are other ways of measuring besides a tape measure - they are called adjectives (there are over 6,000 in the dictionary) so there are 6,000 different types of the emotion of love) in order to draw any conclusions about it.
Personal experiences that cannot be measured by others do not count in science (Lord Kelvin fell over his own statement of this type ... "your knowledge is of a meager
and unsatisfactory kind" he said.
Science can measure what we think are signs of certain emotions, such as body language and
vocalizations (like screaming, whimpering,
howling, etc.). Elephants exhibit many forms of
communication and behaviors that are similar to
things that humans do when we cry or have certain
emotions. These similarities in communication and
behaviors lead many of us to believe that
elephants probably experience similar emotions to humans. However, this is more guesswork (don't you mean personal observation) than science (the social sciences are a science of a sort, just not easily digitalized). In the same way, if my friend says and does the same thing that I do when I am happy, does it automatically mean that she is
happy too? Possibly, but not for sure. (it would be a reasonable expectation) Her body language and communication may be very different from mine, perhaps due to cultural or genetic differences, (stomp on anyone's toes, no matter what language, and the response will be essentially similar) and maybe her signs for frustration are the same as my signs for happiness (nearly an impossibility). Or maybe she is just acting (acting happy by an actress is, temporarily, happy) or pretending to get me to respond in a certain way, but really feels no emotions at all.
When we see other animals (including humans who
act like animals) doing things that look like
certain emotions to us, it is important to realize
that we cannot know or measure (it is measured by
degrees of words (adjectives) called categories)
for certain what emotions they are really
experiencing, if any. That is one of the beautiful
things about emotions: nobody can ever really know
what emotions you are feeling except you (what
about a behavioral scientist or psychiatrist?). They can guess, but if you're a good
actor/actress, you might be able to fool them. The
same goes for elephants. We can never really know
what emotions they are feeling, either. It is very
likely that they experience similar emotions
similar to us, including ones that cause crying.
It is also possible that what appear to be signs
of emotions are really bluffs (bluffing is
legal) or just behaviors that are used to get
other elephants in a group to respond in a certain