Monte Carlo simulations are used to study the equilibrium shapes of unconstrained nematic liquid crystal droplets or tactoids in an isotropic medium. The tactoids are approximately spherical when the mesogen is in its isotropic phase. On cooling into the nematic, the tactoid shape becomes anisotropic, with the symmetry axis aligned along the director. The molecular organisation inside the tactoids is investigated. (C) 2002 Elsevier Science B.V. All rights reserved.