The mechanism for initiation of lateral organs in the shoot apical meristem is still unknown. In this article we investigate one critical component of a buckling mechanism of organ initiation (that is, the presence and distribution of compressive stresses in the meristem). Direct evidence for compression in the sunflower capitulum was obtained from the gaping pattern of shallow cuts and the propagation of fractures. Cuts gaped widely in the central region of the capitulum but remained closed, or nearly so, in the generative and differentiation regions, suggesting the presence of circumferential compression at these locations. Fractures were initiated in the generative region and propagated circumferentially over most of their length. They did not cross the generative region perpendicularly, suggesting again the presence of compressive stresses in the circumferential direction. This conclusion was confirmed by the stress distribution computed from the geometry of the capitulum at three stages of development. One interpretation of these results is that the generative region corresponds to a zone of compression that could control the initiation of new primordia by means of buckling of the tunica layer.