Classical Hall polynomials introduced independently by Steinitz and Hall have a close relation with Hall-Littlewood functions and play important roles in the study of representations of symmetric groups and general linear groups. In the 1990s, Ringel defined Hall numbers for representations of quivers over finite fields and proved that in the Dynkin quiver case, Hall numbers are indeed integer polynomials of the cardinalities of ground fields. We prove that Hall polynomials exist for all hereditary algebras of affine type. This talk is based on joint work with Shiquan Ruan and Lina Han.