Is shell fish a vertebrate or invertebrate?

No, it is an invertebrate. It has no vertebral column which defines "vertebrates".

A mollusc is an animal that comes from the Phylum Mollusca, and could be part of one of 7 classes:

1. Aplacophora
2. Monoplacophora
3. Cephalopoda (like squids and octopus)
4. Scaphopoda
5. Polyplacophora
6. Gastropoda (snails)
7. Bivaliva (clams)

There are 13 general characteristics of the Phylum Mollusca:

1. bilaterally symmetrical, unsegmented, coelomate Protostomes
2. Mantle with shell glands that secrete calcareous epidermal spicules, shell plates or shells
3. body covered by thick epidermal-cuticular sheets of skin, the mantle and mantle cavity (contains the ctenidia, osphradia, nephridiopores, gonopores and anus)
4. large well defined muscular foot, often flatted with creeping sole
5. viscera concentrated dorsally as a "visceral mass"
6. coelom limited to small spaces around the heart and gonads
7. heart lies in pericardial chamber and composed of separate ventricle and atria
8. principle body cavity is hte hemocoel (open circulatory system)
9. buccal region provided with a radula
10. complete gut, with marked region specialization
11. large complex metanephrida ("kidneys")
12. embryogeny typically protostomous
13. with trocophore larva, and usually a veliger larva