Understanding causal regularities in the world is a key feature of human cognition. However, the extent to which nonhuman animals are capable of causal understanding is not well understood. Here, we used the Aesop's fable paradigm - in which subjects drop stones into water to raise the water level and obtain an out of reach reward - to assess New Caledonian crows' causal understanding of water displacement. We found that crows preferentially dropped stones into a water-filled tube instead of a sand-filled tube; they dropped sinking objects rather than floating objects; solid objects rather than hollow objects, and they dropped objects into a tube with a high water level rather than a low one. However, they failed two more challenging tasks which required them to attend to the width of the tube, and to counter-intuitive causal cues in a U-shaped apparatus. Our results indicate that New Caledonian crows possess a sophisticated, but incomplete, understanding of the causal properties of displacement, rivalling that of 5-7 year old children.