Hi,
I'm new here but I have to say that I both agree and disagree with what the others have told you. Brown paper bags can make for a wonderful alternative to newspaper when paper macheing, but you have to know how to do it properly.
First of all, I'd suggest you taking your bags and pulling it apart at the seams. Then, you should crumple it up several times until it's all full of wrinkles and then lay it flat again. Now tear (don't cut) your bag into small pieces, I typically go 1"x1" for highly detailed areas and no larger than 4"x4" for flat non-detailed areas. The reason you want to tear the paper is because it helps to loosen the fibers in the paper and it will help the different layers to stick to each other. I go for a thick, pasty, glue-water solution and I apply it somewhat heavily to the brown paper, using a paint brush to paint it on. I will also suggest using a very fine point brush to smooth the edges of your paper into small cracks and along edges. If you find a piece of the brown paper to stiff or rigid, soak it in the paste to soften it, crumple it some more or discard that piece.
After you have applied a layer or two of the brown paper (letting it dry fully between each layer), you should notice that your piece is a bit heavier and sturdier than if you had applied newspaper. I've had a number of my brown bag mache projects take a beating (or cat knocking them off the top of a bookshelf, repeatedly) over the years and most of them barely have a dent to show for it. You can also get some neat tree bark-like textures out of brown bag mache and a matte finish.
Just remember the trick to making it look good is lots of crinkling, tiny pieces and a tiny paintbrush.