Effects of uniaxial elongational how combined with an external potential field (electric, magnetic) on the isotropic-to-nematic phase transition are considered basing on the Onsager free energy approach and self-consistent field theory. Ellipsoidal particles of uniaxial. symmetry subjected to dipole and quadruple fields are assumed. Mean-field potential of the interparticle interactions accounting for dipole and quadruple contributions is considered. The self-consistency equations include dipole and quadruple contributions of the external and mean-field potentials. The equilibrium thermodynamic potentials, critical conditions of phase instability, and phase equilibria are discussed. Example computations indicate that orientation of rigid, prolate particles in the elongational flow and/or an external potential field results in narrowing the range of phase instability, reducing the difference in orientational order between the phases in equilibrium, and shifting phase equilibria to smaller values of the interparticle interactions parameter. Uniaxial elongational flow contributes a potential with quadruple symmetry, additive to other quadruple terms of the external potential. Specific nature of the flow potential, different to the non-hydrodynamic potentials, is evident in the behaviour of internal energy and entropy. At the phase transitions, the flow contributes to the discontinuity of internal energy and entropy, a term originated from the activation energy of viscous motion. (C) 2001 Elsevier Science B.V. All rights reserved.