Annular structures have been observed experimentally in aggregates of polyglutamine-containing proteins and other proteins associated with diseases of the brain. Here we report the observation of annular structures in molecular-level simulations of large systems of model polyglutamine peptides. A system of 24 polyglutamine chains 16 residues long at a concentration of 5 mM spontaneously formed large beta sheets which curved to form tube-like annular structures that resemble beta barrels. This work was accomplished by extending the PRIME model to polyglutamine. PRIME is an off-lattice, unbiased, intermediate-resolution protein model based on an amino acid representation of between three and seven united atoms depending on the residue being modeled. Our results are interesting not only because of the recent discovery of tubular protofibrils in experiments on aggregation of mutant huntingtin fragments containing expanded polyglutamine tracts but also because Perutz predicted that polyglutamine forms water filled nanotubes.