Kinetics of solidification of phase change materials (PCM) was analyzed for combined heat conduction in the PCM and container wall, and convection in the cold fluid. Stable and convergent numerical methods were derived after transformation to normalized size scale, and corresponding immobilization of the moving boundary. The accuracy was confirmed by comparing numerical solutions and corresponding analytical solutions for control by heat conduction in solidifying layers. The proposed method was used to assess when solidification is controlled solely by conduction in solidified layer, and to analyze relative roles of conduction through the container and convection in the cold fluid. (C) 2010 Elsevier Ltd. All rights reserved.