The purpose of this study was to determine whether the Müller-Lyer illusion is produced by a mechanism which uses information defined in the retinal coordinates, or by a mechanism taking into account the three-dimensional (3-D) shape of the illusion figure. The classical Müller-Lyer figure could not be used to address this question since it is two-dimensional. Three-dimensional Müller-Lyer figures were created to see if the illusion they produce is correlated with the shape of the projected retinal image, or with the shape of these figures defined in a 3-D coordinate frame. In the experiments retinal image shape was juxtaposed against the 3-D shape of the illusion displays. For some displays the direction in which the fins pointed, relative to the shafts, in the 3-D frame was the "opposite" of the direction in which they pointed in the retinal images. For such displays, the illusion predicted on the basis of the 3-D structure was the opposite of that predicted on the basis of retinal image shapes. For another 3-D display the fins were oriented such that each projected a single straight line in the retinal image, thus the typical retinal image (< >, > <) was replaced by straight lines (symbol: see text). For all the displays the observed illusion was consistent with how the fins were oriented relative to the shaft in the 3-D coordinate frame, ie with the 3-D shape of the illusion displays. The retinal image shape appeared to play little, if any, role. One conclusion that emerges is that the specific retinal image shape projected by the classical line-drawn pattern is neither necessary nor sufficient for producing the illusion. The present findings are inconsistent with two well known theories of the Müller-Lyer illusion: inappropriate constancy scaling and selective filtering.