Based on the ultrasoft pseudopotential technique of the Vienna ab initio simulation package, we performed ab initio calculations for the (100), (110), and (111) surfaces of CoSi2 within the framework of the generalized gradient approximation. Surface energies were derived from the total energies as well as estimated from simple models. Relaxed surface geometries were determined for the (1X1) surfaces by force minimization. For the (100) surface a proposed root 2x root 2 reconstruction was investigated that, however, is not stable. Energetical results as well as simulated scanning tunneling images strongly indicate that the reconstruction does not exist. The band structures show a number of surface stares, in particular, in gaps of the projected bulk bands at and above Fermi energy for the (100) and (110) surface. For the Si-Co-Si terminated (111) surface, however, only two Si-like surface bands are found. Some surface states are analyzed in terms of density contours revealing covalent Co-Si bonding and coupling to deeper layers. Work functions are also provided. [S0163-1829(98)01307-1].