Melissus’ fragment B9, where he claims that being has no body and no thickness, raises the question of how being can be extended and full and at the same time incorporeal. Most recent interpretations tried to avoid lending to “body” the meaning of “physical body”. My aim in this paper is to reconstruct Melissus’ notion of body, by examining its connection to “thickness”. I show that Melissus meant by “thick” something that has distinct parts and therefore supports in B9 the (...) indivisibility of being. I then indicate that he relied on the contrast between soul and body for his conception of corporeality, by highlighting that by Presocratic thinkers, the soul was considered as “thin” and regarded as something that could be exempt of the division into parts. I conclude that even though Melissus’ notion of incorporeality is very different from the one Plato will develop, he made a huge step toward its conceptualization. (shrink)