The pathological manifestation of nine hereditary neurodegenerative diseases is the presence within the brain of aggregates of disease-specific proteins that contain polyglutamine tracts longer than a critical length. To improve our understanding of the processes by which polyglutamine-containing proteins misfold and aggregate, we have conducted molecular dynamics simulations of the aggregation of model polyglutamine peptides. 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. The effects of hydrophobicity on the system are studied by varying the strength of the hydrophobic interaction from 12.5% to 5% of the hydrogen-bonding interaction strength. In our simulations, we observe the spontaneous formation of aggregates and annular structures that are made up of beta-sheets starting from random configurations of random coils. This result was interesting because tubular protofibrils were recently found in experiments on polyglutamine aggregation and because of Perutz's prediction that polyglutamine would form water-filled nanotubes.