Lucretius’ Epicurean manifesto De rerum natura includes criticism of different aspects of ancient culture, such as classical mythology. Although from the textual evidence it is indisputable that he criticises the traditional Roman religion and its customs, the claim, defended in this article, that Lucretius was a religiously deviant thinker in a potentially harmful way for the ruling elite is controversial. It is controversial because there was, to some extent, freedom of religion in the late Roman republic. However, I argue that those in power had weighty reasons to consider De rerum natura as a religiously deviant work and thus Lucretius as an impious thinker (i.e., a person who lacks reverence towards the Roman gods and religious traditions). To be precise, his views are, even in the Roman intellectual context, radical. I use Varro’s theologia tripertita (‘threefold theology’), the sociological definition of religious deviance by Fritz Sack and John Scheid’s terminology of Roman religion to analyse Lucretius’ position.