  The canonical bases of cluster algebras of finite types and rank 2 are given
explicitly in \cite{CK2005} and \cite{SZ} respectively. In this paper, we will
deduce $\mathbb{Z}$-bases for cluster algebras for affine types
$\widetilde{A}_{n,n},\widetilde{D}$ and $\widetilde{E}$. Moreover, we give an
inductive formula for computing the multiplication between two generalized
cluster variables associated to objects in a tube.
