The solidification of a thermally supercooled liquid in stagnation-point flow is investigated. Due to the advancing solidifying front, both the temperature and flow fields are time dependent. A numerical solution to the problem using an interface tracking method is compared to analytical solutions obtained for instantaneous similarity (short time solution) and quasi-steady state (long time solution). The results show that the velocity of the solid-liquid interface eventually reaches a constant value and that the magnitude of the interface velocity increases with greater thermal supercooling. The solution to this problem provides insight into more complicated solidification problems relating to crystal growth. (C) 2003 Elsevier Ltd. All rights reserved.