Also, you will almost never meet a "fancy" cat breed in a shelter or rescue. About 95% of cats are simply domestic (not mixed), meaning they are no particular breed. The cat is even less likely to be purebred if you find him/her in a shelter.
She appears to be a lovely domestic longhair! I can't quite tell from the pictures if she's black in color, or dark blue (gray). In the second picture she looks like a blue cat, in the first picture it's not clear.