I have a medium framed Hopkins and Allen falling block rifle chambered for .38XL Shotgun. I know the takedown procedure, which is much like most other little single shots, but I need help. 
When I remove the takedown lever, the barrel wont budge. I built a homemade slidehammer, and dropped a covered rod through the barrel to try and jar it loose, but the barrel wont budge. The gun is pretty nice, and I don't HAVE TO take the barrel off, but I'd sure like to.
Anyone have any suggestions on how I might coax the barrel off? It acts like it may have never been off the gun.
Thanks,
Vall

mine was rusted in too-no the barrel is not threaded in. I presume you removed the takedown lever on the side? Put the receiver in the bench vise w/soft jaws-tight, open breech, get a large punch(3/8 or 1/2") and hit the end of the 
barrel shank a few lusty blows with a HEAVY hammer. That should do it. I tried heat and it didn't work, and i twisted the barrel with a heavy wrench, but that did not work either.I don't like heat-you can ruin the heat-treatment if you get it too hot-and some persons think these are weak actions anythy.

I would try to soak the action/barrel joint in good penetrating oil such as Kroil for a few days.  The barrel will probably come off easier without damage.

Coupla things. First, thermal cycling as hst suggested, accompanied by application of penetrating oil/Kroil, has proven to be the most successful IMO & IME. A small propane torch is handy, inexpensive and also unlikely to heat things up too much for safety. The proper bbl vise & jaws plus a good receiver wrench will provide a safe way to break the rust bond, by twisting, without worrying about damaging things. BTW this thermal cycling also works for removing bbls installed with Loctite, as some Benchrest smiths have been doing lately.

Second, a length of PVC pipe of an appropriate diameter, properly plugged on one end, makes an economical reservoir for soaking parts in most penetrating oils & some solvents. After all, you really need to soak only the action ring & bbl stub, so choose the minimum diameter pipe & fill it only as high as necessary to cover the receiver & the first inch or so of the bbl's chamber area. After soaking is complete, the remaining liquid can be decanted into a different (marked) container. DO NOT return the now-dirty oil or solvent to its original container, to avoid contamination, and DO mark the container of the now-dirty liquid. You can use it over & over if you keep it sealed to avoid evaporation.
HTH, Joe