Ah...a lot of info above is wrong.
Short Barrel Rifles (SBRs), Any Other Weapon (AOWs) and Short Barrel Shotguns (SBS) are all legal in MA. Suppressors are not and I have no idea about explosives and incendiary devices.
A 'Green Card' is only necessary for a machine gun, nothing else. In fact, you could theoretcially just have a green card and own a machine gun but not have an FID or class A or B permit.
Similarily, you can own a SBR with only a class B license. For example, if you have a Ruger 10/22 and wanted to cut the barrel down to 10', it is legal in MA assuming you have class B or better (to own the rifle) and you get your CLEO to sign off on your Federal paperwork.
If you are requesting legal help over the web, understand that you will get a lot of poor, incorrect information. The idiots in the MA legislature have no idea and don't take the time to understand what an SBS, SBR or an AOW is or they probably would have banned it by now.
Also, keep in mind that States laws and Federal laws don't always make sense. You don't need a 'Green Card' for class 3 material, but rather only for Machine Guns, which happen to be a type of class 3 items. Then you have to jump through your CLEOs rules and assuming you get through all three hoops you get a new toy.
Finally, if you are serious about getting into class 3 weapons, then go talk to a dealer (I recommend these two - Waltham: Law Enforcement Equipment or Norton: We Are Guns) and ask them what you need to buy the AOW, SBR or Machine Gun you want. They dealers know the laws (they want the sale) and then you schedule a meeting with your CLEO to let them know you are interested in a purchase and that the dealer has walked you through the State laws. Then you ask if the CLEO will confirm with his signature that it is legal to own the type of weapon in question in his jurisdiction and wait to see if the CLEO has any particular rules (must have a safe, alarm, etc.) but don't bring this part up - let the CLEO tell you. Then schedule a follow-up with your paperwork and proof of complicance with the chief's regulations.
When I first got into class 3 toys, I spoke with Richard at We Are Guns about buying a Mossberg AOW - got my facts straight and setup a meeting with my CLEO. After my meeting with my CLEO and learning that he would sign b/c I'm a responsible person, I came back with the proper paperwork for an SBR, an AOW and a Green Card application. He signed all three, but I later had to get my C&R license from the Feds to complete the Green Card application. My MA state examiner rejected my Green Card application since my examiner didn't consider me a valid "collector" because I didn't have a Federal C&R license. A C&R is very easy to get - you send in the Fed paperwork and it comes back with 20 lbs of books in about 2 months. Once I gave the examiner my C&R license number, I was sent my Green Card. By the way, my Green Card says "For All Lawful Purposes", but that is another story.
Yes, my CLEO was good to work with, but if you believe everything you read on the web you wouldn't think you had a chance in hell of getting any - much less three signatures on class 3 toys in MA. I've since moved to NH, but the moral of the story is talk to people who have completed the transaction - not the people who are "pretty sure MA prohibits"
Good luck and spread the word so more people buy class 3 toys before the legislature bans them!