This document describes the conceptual design for the Offline Software and Computing for the Deep Underground Neutrino Experiment (DUNE). The goals of the experiment include 1) studying neutrino oscillations using a beam of neutrinos sent from Fermilab in Illinois to the Sanford Underground Research Facility (SURF) in Lead, South Dakota, 2) studying astrophysical neutrino sources and rare processes and 3) understanding the physics of neutrino interactions in matter. We describe the development of the computing infrastructure needed to achieve the physics goals of the experiment by storing, cataloging, reconstructing, simulating, and analyzing ∼ 30 PB of data/year from DUNE and its prototypes. Rather than prescribing particular algorithms, our goal is to provide resources that are flexible and accessible enough to support creative software solutions and advanced algorithms as HEP computing evolves. We describe the physics objectives, organization, use cases, and proposed technical solutions.