We report the dependence of the ferroelectric domain configuration and switching behavior on the shape (square versus round) of epitaxial BiFeO3 (BFO) nanostructures. We fabricated (001) oriented BFO(120 nm)/SrRuO3(SRO,125 nm) film layers on (001) SrTiO3 single crystals by rf magnetron sputter deposition, and patterned them to square (500×500 nm2) and round (502 nm in diameter) shaped nanostructures by focused ion-beam lithography. The surface morphology and the crystalline structure of the nanostructures were characterized by scanning electron microscopy and x-ray diffraction, respectively, while the domain configuration was investigated using piezoelectric force microscopy. We found that the square-shaped nanostructures exhibit a single variant domain configuration aligned along the  direction, whereas the round-shaped nanostructures exhibit seven variants of domain configuration along the , , , , , , and  directions. Moreover, local d33 piezoelectric coefficient measurements showed hysteresis loops with a strong displacement in the voltage axis (strong imprint) for the square-shaped nanostructures, while the round-shaped ones exhibited more symmetric loops. These findings have critical implications for the development of nanocapacitors for gigabyte to terabyte nonvolatile - ferroelectric memories.