We study the electronic properties of a mesoscopic system composed of an array of straight, infinite rods made of an isotropic medium and embedded in a regular way in an isotropic background. Such a composite system has two-dimensional periodicity in the plane perpendicular to the rods. Using a Fourier series expansion, the corresponding Schrodinger equation is solved within the effective-mass approximation. The electronic band structure E = E(k) is computed for the wave vectork in the transverse plane, and is illustrated by dispersion curves along the principal directions of the two-dimensional Brillouin zone as well as by the histograms of the density of states. The main result is the appearance of absolute energy gaps in the two-dimensional band structure.