By performing epitaxial growth of Ge on Si(113) layer by layer, observed using scanning tunnelling microscopy, we show the Ge/Si(113) surface structure and island shape transition with an increase of Ge coverage and we discuss the transition in terms of epitaxial stress evolution and relaxation of the epitaxial morphologies. Nanofeatures of Ge epitaxial islands, such as nanowires and nanodots, are highlighted.