expungment

What is the name of your state (only U.S. law)? mississippi

i have had a couple of felony arrests in which the charges were dropped, how would one get these arrests expunged so that when a background check is done they will not be found?

You apply to the court.

Miss. Code 99-15-26(5)

Upon petition therfor, the court shall expugne the record of any case for which an
arrest was made, the person arrested was released and the case was dismissed or the charges were dropped or there was no disposition of such case.