We present the results of a first-principles pseudopotential plane-wave study for the structural properties of the ε-FeSi (B20), NaCl (B1) and CsCl (B2) structures of FeSi. The calculations were performed using the local density and the generalized gradient approximations (LDA and GGA), for the exchange-correlation potential. The electronic structures of the B1 and B2 phases have been similarly investigated. These calculations have enabled us to identify the driving force behind the crystallization of FeSi in the B20 phase. Both the B1 and B2 phases are found to be semimetallic, with the Fermi energy lying in a pseudo-band-gap. The B20 structure is predicted to become unstable with respect to the B2 phase at a moderate pressure, of 13.5 and 10.9 GPa according to the GGA and LDA calculations, respectively.