The mass transfer in a liquid cylindrical inclusion migrating normally to close-packed planes of a non-uniformly heated crystal under the stationary thermal conditions has been analyzed theoretically. The developed model of the mass transfer takes into account anisotropic interfacial energy density, anisotropic interface kinetics, and capillary effects. The dependences of both the inclusion velocity and the cross-section shape on the cross-sectional area, the temperature gradient, the interfacial energy density, and the interface kinetics parameters have been calculated and discussed. It has been shown that (1) the reason of deviation in shapes of migrating inclusions from equilibrium ones is the interface kinetics limiting the mass transfer in the liquid; (2) the interface kinetics generates the dependences of the shape distortion on the temperature gradient, the cross-sectional area, and the interfacial energy density; (3) the temperature-gradient dependences of the inclusion shapes are significantly different for the cases of the screw-dislocation and two-dimensional (21)) nucleation mechanisms of interface processes; (4) the mass transfer in the cylindrical inclusions is almost not limited by the growth kinetics at the singular interface, and, therefore, the cylindrical inclusions migrate faster than the liquid layers of the same thicknesses; (5) distortion in cross-section shapes of migrating inclusions is not an unambiguous function of their velocities. (c) 2008 Elsevier B.V. All rights reserved.