The first results of optical interband investigations are reported for semiconducting Ru2Si3 from the near infrared up to 5 eV and compared with those of a Ru metal. The single-phase Ru2Si3 layers were prepared by metal deposition onto silicon substrates and annealing in forming gas atmosphere. The optical spectra have been obtained by ellipsometry and reflectivity measurements. From the optical investigations, the real and imaginary parts of the dielectric function as well as the absorption coefficient and the refractive index have been derived. The Ru spectra show typical metallic behaviour, i.e. a Drude-like shape in the IR and interband features at higher energy. The spectra for Ru2Si3 exhibit semiconducting character with dominant interband features approximately at 2 and 5 eV and a relative minimum in the joint density of interband states at 3.5 eV. These spectra are compared with theoretical calculations of the optical properties which have been carried out using the LMTO-ASA method. Excellent agreement has been found between theory and experiment for the spectral variation in the optical constants.