This document presents a variant of the Ordinary λ-Calculus that we call the Distributed λ-Calculus. The novelty is in addition of node annotations to terms in addition to a mobility rule. We show that, despite distributed programs, the Distributed λ-Calculus is computationally equivalent to the Ordinary λ-Calculus. That is of special importance becasuse, despite the common belief, distributed programming can happen without side-effects. A significant shortcoming of the Distributed λ-Calculus is that it does not model interaction with the real world. In other words, it only models programming a closed distributed system.