ZnO nanowires with different sizes and geometrical shapes have been studied by means of density functional theory (DFT) calculations. Atomic relaxation, energetic stability, and electronic properties of these nanostructures show a particular dependence on the shape of the nanowires. Our results indicate that the hexagonal shape nanostructures are more favorable than the triangular one due to lower total surface energy, whereas lattice relaxation and surface states appear to be more pronounced in the case of triangular nanowires.