In many states, a felony conviction can't be expunged otherwise every criminal would be walking around w/o a record. Talk to your attorney about the specifics for your state. Chances are that if it is possible to have your record expunged, it will be a few years before it's permissable.
Various statutes provide for expungement of criminal records. Generally, the records are not destroyed but are sealed and made available only to law enforcement and judicial officials. However, expungement means destruction of the records.