Are you talking about rifle plates that are worn in conjunction with soft armor, like the plates that go in the IBAS? Or are you talking about the trauma plates that are ususally used in conjunction with concealable body armor to give a little added protection to the heart area?
From your description of an inch or so of padding, it sounds like you're talking about a stand alone rifle plate. That's not plastic padding but kevlar.
Rifle plates come in two types, stand alone (which means they can be used without any other armor) and plates that are made to be worn with level IIIa soft armor. The plates can be made of steel, titanium, ceramic composites and even plastic.
Jeff