Tau is one of the diverse group of microtubule-associated proteins that bind to microtubules and may thereby influence their structure and function. It occurs in the mammalian brain¹, mainly in axons, and is a component of the neurofibrillary tangles of Alzheimer's disease^2,3. Tau was recently sequenced⁴, but there remains a shortage of structural data on the protein. We have now prepared paracrystals of tau suitable for electron microscopy and image processing. They show distinct transverse banding and polarity, indicating that the protein subunits are aligned with the same orientations. In contrast to other paracrystals, those of tau protein can stretch or contract continuously by more than three-fold; the axial repeats range from 22 to 68 nm. After scaling to a common period, the density distributions are closely superimposable. This suggests that tau is an elastic molecule.