Snakes belong to the phylum Chordata. This phylum includes all animals that have a notochord at some stage in their development. The notochord is a flexible, rod-shaped body that provides support in the embryonic stage. In snakes, as in other vertebrates, the notochord is replaced by the vertebral column (spine) during development.
Within the phylum Chordata, snakes are further classified into the class Reptilia, which includes all reptiles. Reptiles are characterized by their scaly skin, cold-blooded metabolism, and typically laying shelled eggs on land.
So, to summarize, the phylum of a snake is Chordata, and it falls under the class Reptilia.