Hi,
Which cell phone do you have? As different sets are having different process on same thing. Still you will try one thing i will suggest you-
just go to the message box and select the message you want to delete. May be when you touch the screen for select the message you want to delete, it shows a option "Delete Thread" or "delete". If it is then click on this option. Your message will be deleted. Otherwise please specify first, which cell phone you are using...