All of the things I have read do classify sharks as vertebrates because they do actually have backbones. As you can see from the link I've included below, sharks are classified as chondrichthyes, as kind of fish. This classification is part of phylum Chordata -- the vertebrates.
If you have read something that classifies a shark as an inveertebrate it is probably because the shark's backbone is not actually made of bone. Sharks do not have any bones. Instead, their skeletons are made up of cartilage, which is the stuff that makes your ears stiff but bendy.