A particle approached by an advancing solidification front may be set in motion under the influence of forces that act across the narrow gap between it and the advancing solidification front. This particle motion induces a drag that promotes engulfment of the particle in the advancing solidifying medium. This drag force experienced by a particle being steadily pushed by a solidification front is studied numerically. A sharp-interface method is used to track both the phase boundary and the particle. The method employed in this paper allows for inclusion of the effects of thermal property differences between the particle and the melt. The dependency of the drag on the thermal conductivity ratio of the particle to the melt, as well as on the thickness of the thin gap between the solidifying interface and the particle, is examined. The results of the present calculations are compared with those of previous analyses. It is shown that previously used expressions for the drag on a particle may not correctly account for the effects of thermal conductivity of the particle. (C) 2004 Elsevier B.V. All rights reserved.