Understanding the mechanisms underlying the assembly of nucleobases is a great challenge. The ability to deeply understand how nucleobases interact with themselves as well as with other molecules will allow us to gain valuable insights into how we might be able to harness these interesting biological molecules to construct complex nanostructures and materials. Uracil and thymine derivatives have been reported for use in biological applications and in self-assembling triple hydrogen bonded sys- tems. Either uracil or thymine possesses three binding sites (Site 1, Site 2, and Site 3) that can induce strong directional N-H···O=C hydrogen bonding interaction. In this paper, theoretical calculations are carried out on the structural features and binding energies of hydrogen-bonded dimers and trimers formed by uracil and thymine bases. We find that the hydrogen bonds formed through Site 1 are the strongest, those formed through Site 3 are next, while those formed through Site 2 are the weak- est. The atoms in molecules analysis show that the electron densities at the bond critical points and the corresponding Laplaci- ans have greater values for those hydrogen bonds formed through Site 1 than through Site 2. All these results indicate that a uracil (or thymine) would interact with another uracil or thymine most likely through Site 1 and least likely through Site 2. We also find that a simple summation rule roughly exists for the binding energies in these dimers and trimers. Understanding the mechanisms underlying the assembly of nucleobases is a great challenge. The ability to deeply understand how nucleobases interact with themselves as well as with other molecules will allow us to gain valuable insights into how we might be able to harness these interesting biological molecules to construct complex nanostructures and materials. Uracil and thymine derivatives have been reported for use in biological applications and in self-assembling triple hydrogen bonded sys- tems. Either uracil or thymine possesses three binding sites (Site 1, Site 2, and Site 3) that can induce strong directional NH ··· O = C hydrogen bonding interaction. In this paper, theoretical calculations are carried out on the structural features and binding energies of hydrogen-bonded dimers and trimers formed by uracil and thymine bases. We find that the hydrogen bonds formed through Site 1 are the strongest, those formed through Site 3 are next, while those formed through Site 2 are the we ak-est. The atoms in molecules analysis show that the electron densities at the bond critical points and the corresponding Laplaci- ans have greater values ​​for those hydrogen bonds formed through Site 1 than through Site 2. All these results indicate that a uracil (or thymine) would interact with another uracil or thymine most likely through Site 1 and least likely through Site 2. We also find that a simple summation rule roughly exists for the binding energies in these dimers and trimers.