Huckel simulations of large finite graphene nanomeshes with lithographically induced holes show sizable band gaps in the conduction while the optical absorption has generally the same semi-metal character as pure graphene. There is a strong dependence of the band gap on the angle between the graphene axis and the periodic hole axis. Simple modification of on-site energies shows that substituents on the edges of the holes could also have a significant effect. These simulations show that graphene nanomeshes, which have been recently fabricated, are potentially useful tunable materials for electronic applications. (C) 2010 Elsevier B.V. All rights reserved.