Michelin invented the radial in 1946 and steel has been the material of choice since then. The steel belts is why it's so important to have punctures sealed properly. Water getting into the belts rusts them, which can lead to tread separations.
The worst radial tire ever made was the Firestone 500 of the 1970s. They blew up REAL good.
my motorcycle tires are nylon belted, they might have steel in the bead, but that's it, it should say the ply raiting on the side wall, but I don't think the ply number is truely how many layers of belting it has, but insted it's "as strong as" that many plys... but they normaly tell the number of nylon, and the number of steel in the tire.