A p-adic subanalytic set shares with a real subanalytic set the fundamental property that its singular locus is itself subanalytic. Furthermore, given a p-adic subanalytic function ƒ with domain contained in ℤ, there is an integer L such that for any point x ∈ ℤ in a neighborhood of which f is defined, f has a Taylor approximation up to order L at x if, and only if, ƒ is analytic around x . These results extend to the p-adic fields real variables theorems by M. Tamm [21].