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Visual artists can be considered the precursors of students of the visual system. Paintings and graphic arts have been attentively examined by vision scientists, while sculpture has been considered less. Here we intend to fill this gap by illustrating how artists faced what seems an impossible challenge: to carve a stone so that it looks like a transparent veil. The success of the artists in reproducing the veil can be assessed by exploring the hundreds of Internet pages dedicated to ‘veiled statuary’. We chose some of the most admired statues and tried to ‘glean’ the sculptor’s technique. Two of these artworks are the work of Greek artists, the other statues were carved by baroque and modern sculptors. We did not find a single technique but, rather, a diversity of solutions, as is to be expected in an exploration in which opposites must be reconciled: an observer has to catch the presence of something elastic, thin, and transparent in a surface made of a rigid and opaque material. We checked the ability of the sculptor to render such properties by submitting samples of veiled statues to some observers who were asked to judge the strength of the veiling effect, and to categorize the perceived materials and features, such as transparency and thinness. The results confirm the artists’ knowledge of visual cues that are able to convey a complex set of information and meanings: material categorization, materials properties, perceptual decomposition of surfaces, completion of perceptual fragments into unitary percepts.