This procedure may be helpful to you:

Instructions

       1

       Launch Mozilla Thunderbird on the computer.
       2

       Click "Tools" and then select "Account Settings" from the drop-down menu.
       3

       Click the relevant email account in the left pane of the program window.
       4

       Click "Copies & Folders." Find the "Drafts, Archives and Templates" section in the "Copies & Folders" settings page.
       5

       Look under the "Keep Message Archives" heading. You'll find the archive folder location in the dialog box below this heading.
       6

       Access archived messages by clicking on the archive folder from the left pane in the main program window.

Read more : http://www.ehow.com/how_8320625_archived-messages-thunderbird.html

I followed all the steps, changed the Archive location to Local Folders but the only two folder I see is Trash and Outbox.

Here is another method:

To open a folder you have archived:

   Make sure Mozilla Thunderbird is not running.
   Open your Mozilla Thunderbird profile directory.
   Go to the Mail folder.
   Drag and drop the archived folder file (Archive, for example) from its remote location to the Local Folders folder.
       Make sure you do not overwrite existing files.
       If a file with the same name already exists under Local Folders, rename the archived folder file before copying. 
   Open Mozilla Thunderbird.
       The archived folder should appear under Local Folders in the folder list. 

If you don't know how to open your profile directory, let me know.

I do not know how to open my profile directory

Check the View menu (Alt+V) has folders set to all. Before you changed the settings for archive, where did it point to? changing the location foes not move anything, so you need to identify where it was.

Is this an IMAP account? in which case you may not be subscribed to the archive folder. Right click the account on the left and select subscribe.

oh and to open your profile folder (if you really need to) Help menu (alt+H) > troubleshooting information and click the show folder button then close Thunderbird.

I will bow out to Matt if he is going to help you.

I did the steps you told me to do and I closed Thunderbird. I saw a list of folders but no Archive folder.

PS - At home I use Gmail and have it go to my MS Outlook. Since some at the office use Thunderbird, I thought that I will try Thunderbird at home. All my e-mails were exported correctly (even some of the folders). My addresses were exported correctly. So far so fine.

But I can not get my Archive, a feature that I wan to try. All the suggestions that I have received have not been successful.

I have found how to locate your archived messages. I haven't done this, so I can't follow through to check.

Open Thunderbird. Right click on your account name in the left pane. Click on settings. Click on copies and folders. In the centre of this box, it tells you where your archived messages are located.

Hopefully, this will help.

I finally got it to work!!! Thanks to all for your valuable assistance. It must have required a lot of your patience to solve my problem.