Roof Coverings

I am wondering what to use for my water tight roof. I have an addition on my home with a flat roof and when I had the old black rubber removed they put down a white vinal materal similar to flooring, Has anyone ever used any vinal type of roofing materals glued down? Shrinkage problems? I am not sure what I want to do. It comes in a 10 foot wide roll and is about 1/8 thick and very bendable. Any suggestions from the old veteran builders would be great!!! Thanks Bill