Absorption spectra of nanosized spherical silver particles hexagonally arranged in planar arrays have been calculated using the discrete dipole approximation (DDA). The silver dielectric function used in the calculations is size-corrected in order to account for the ultrafine particle size of 5 nm in diameter. The optical anisotropy arising from the dimensionality of the planar array of close-packed nanoparticles is clearly revealed in the absorption spectra by the splitting of the surface plasmon resonance (SPR) in two bands corresponding to the longitudinal and transverse modes. Under p-polarized light, the amplitude of the splitting is observed to sensitively increase for decreasing interparticle spacing. This behavior makes it possible to well distinguish the two SPR bands under the requirement that the interparticle spacing should be smaller than around one particle radius. Indeed, for larger interparticle spacing, the two plasmon modes tend to superimpose, so that the profile of the resulting single band looks nearly the same as the one of an isolated nanoparticle.