Abinitio molecular orbital calculations are reported for the optimum structures of many free radicals, including several species in which the central atom is hypervalent, and for some triplet states. Most geometries are close to those predicted by the VSEPR method for molecules with one additional electron, with the unpaired electron occupying a "lone pair" position. Deviations from the ideal geometries of hypervalent radicals can be rationalized in terms of different strengths for repulsions between electrons of different types. Alternatively the geometries can be understood by using the three-centre, four-electron bond theory for the hypervalent species and the σ-conjugation concept for the non-hypervalent molecules. The distortions from ideality of the hypervalent structure occur to allow interaction of the electron pair of the nonbonding MO of the three-center unit to interact with a lobe of the unpaired electron's orbital. Keywords: geometry of free radicals, abinitio MO theory for radicals, VSEPR theory for radicals, sigma conjugation for radicals.