The soft-bodied Ediacara biota (571-541 million years ago) represents the oldest complex large organisms in the fossil record, providing a bridge between largely microbial ecosystems of the Precambrian and the animal-dominated world of the Phanerozoic, potentially holding clues about the early evolution of Metazoa. However, the nature of most Ediacaran organisms remains unresolved, partly due to their enigmatic non-actualistic preservation. Here, we show that Flinders-style fossilization of Ediacaran organisms was promoted by unusually prolonged conservation of organic matter, coupled with differences in rheological behaviour of the over- and underlying sediments. In contrast with accepted models, cementation of overlying sand was not critical for fossil preservation, which is supported by the absence of cement in unweathered White Sea specimens and observations of soft sediment deformation in South Australian specimens. The rheological model, confirmed by laboratory simulations, implies that Ediacaran fossils do not necessarily reflect the external shape of the organism, but rather the morphology of a soft external or internal organic 'skeleton'. The rheological mechanism provides new constraints on biological interpretations of the Ediacara biota.