I think I know what you're saying.  But I think you may be worrying about the finished surface too early in the project.

I would get the paper attached to the styrofoam so you get the basic shape of the dog as you want it.  Let it dry, then do any strengthening that is necessary, & fill in any gaps.

Are you using pulp papier mache on the final surface, or just the paper strips?  (You can do either one, or both.) 

When you've got the dog properly formed and you are working on the final exposed surface, that is the time to smooth out the finish.  You should have enough layers that when the whole thing is dry, you can use sandpaper wrapped around a piece of wood to smooth off the wrinkles, curled up ends and little lumps.

After you make sure that the entire project is thoughly dry (all the way through), I would cover the entire surface with painted on gesso, or white acrylic paint carefully thickened with some whiting (also known as powdered chalk or calcium carbonate), or some kind of thick paint primer (used on walls) to smooth out the surface.  When that is dry, run your hands over it the surface and feel for any lumps that need a little more sanding.  Use your gesso (or whatever) on any places that you've just sanded and let it dry THOROUGHLY.  Then paint the dog as you wish.  You may also want to seal it.

And your English is VERY good!

Sue

What did you use for the styrofoam base?  Blocks?  Sheets?  Foam?  How did you put it together?  I'm working on cats, from small to huge, and soon I'll need to craft a large one.  (Still a newbie and needing all the help I can get. )

Vinca, I used sheets of foam. These were smaller than the project I had in mind so I laid them side by side on the floor, drew the dog on them and cut out the shape. I glued the parts on a second layer of sheets using acrylic paint* and large screws, which I took out after the paint had dried. I cut out the shape on the second layer, glued on a third layer.. and so on until I had about 10 layers. I used as many leftover parts of foam as I could, but still had lots of pieces left which is a shame because this stuff is really bad to the environment. It can be recycled though, but the people at the place where you can bring your trash (sorry i don't know how this is called) couldn't tell me wether it would be recycled or burnt.

Anyway, when the object was thick enough I sculpted it using a knife. I also sanded it using a flat sanding tool which gave a huge mess! You should really protect your nose, mouth and eyes when you do.

The shape of my dog is really simple so it was easy to do this, I have some pictures here: http://members.home.nl/golan-ingrid/dog.html
you can clearly see the sheets of foam thanks to the paint I used as glue.

*I used acrylic paint because I was lacking money to buy special styrofoam glue. It worked well, especially with the aid of screws, but it gave some problems when sanding because it is easier to sand the foam than to sand the glue, so you'll get lumpy bits. I don't know if this special glue does the same thing.

Did i see a picure of one of your cats in an earlier topic? it looked really nice. i hope my information was helpful to you. good luck!

Another option is to use paper towels instead of newspaper or paper towels on top of the newspaper.  Paper towels are stronger and have more stretch than newspaper.  The only problem is that they are not as rigid.  Bot you will get better corners and the seems won;t show.

I tried using thick paper for the corners and it worked really well! I teared 160gr paper into strips and soaked them with glue, then folded them into the corners. They turned out really straight. The next problem I now have is the seams of this thick paper, but it's easier to solve that than the wrinkly paper I had earlier! Thanks so much for thinking along!