We prove that the finite-model version of arithmetic with the divisibility relation is undecidable (more precisely, it has Π 0 1 -complete set of theorems). Additionally we prove FM-representability theorem for this class of finite models. This means that a relation R on natural numbers can be described correctly on each input on almost all finite divisibility models if and only if R is of degree ≤ 0 . We obtain these results by interpreting addition and multiplication on initial segments of finite models with divisibility only.