Si(113) is of potential technological interest because it is thermally stable and appears to be a promising substrate for heteroepitaxy. However, existing models of its atomic structure do not agree with experimental findings. We present a new model of Si(113) which is based on a novel idea of a subsurface self-interstitial. Guided by STM measurements and ab-initio calculations we find a structure which is stable, reproduces STM images, and allows for the observed transitions between 3 x 2 and 3 x 1 phases. Moreover, we show that a careful energy optimization of atomic positions is needed for a reliable interpretation of STM images.