Looking on the internet deeply has found these results:

one of my friends' is the most popular phrase on the web.

one of my friend's 10 results on the web	one of my friends' 1730,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
law, who is from the east, helped me with husking, using a huge 'scary looking' cleaver/scythe. Boots. I'm staying at one of my friend's. in A Luckily for me one of my friend's father One of my friend's parents invests in startups, and he loves Peek "Life is everything I dreamt it would be" one of my friend's Facebook status' boldly proclaimed.	First one is right..one of my friends. Similarly one of the famous lawyers is correct. When you say "one of the" you indicate a particular one from many.so it has to ... Actually, I had thought that "a friend of mine" sounded more natural than "one of my friends." Now I have understood that I can use both of them. Thank you again ... Jul 2, 2011 ... It's "one of my friends". The other option would be ungrammatical. To spice it up a little, here are the stats from the Corpus of Contemporary ... Jun 29, 2012 ... Or is it grammatically wrong to have such a possessive construct and the correct form is: The father of one of my friends is serving in the Navy.

one of my friend's

10 results on the web

one of my friends'

1730,000 results on the web

More popular!

law, who is from the east, helped me with husking, using a huge 'scary looking' cleaver/scythe.
Boots.
I'm staying at one of my friend's.
in
A
Luckily for me one of my friend's father
One of my friend's parents invests in startups, and he loves Peek
"Life is everything I dreamt it would be" one of my friend's Facebook status' boldly proclaimed.

First one is right..one of my friends. Similarly one of the famous lawyers is correct. When you say "one of the" you indicate a particular one from many.so it has to ...
Actually, I had thought that "a friend of mine" sounded more natural than "one of my friends." Now I have understood that I can use both of them. Thank you again ...
Jul 2, 2011 ... It's "one of my friends". The other option would be ungrammatical. To spice it up a little, here are the stats from the Corpus of Contemporary ...
Jun 29, 2012 ... Or is it grammatically wrong to have such a possessive construct and the correct form is: The father of one of my friends is serving in the Navy.