[en] Recently available experimental data indicate that the solidification of undercooled molten silicon prepared by pulsed laser melting of amorphous silicon is a complex process. Time-resolved reflectivity and electrical conductivity measurements provide information about near-surface melting and suggest the presence of buried molten layers. Transmission electron micrographs show the formation of both fine- and large-grained polycrystalline regions if the melt front does not penetrate through the amorphous layer. The authors have carried out extensive calculations using a newly developed computer program based on an enthalpy formulation of the heat conduction problem. The program provides the framework for a consistent treatment of the simultaneous formation of multiple states and phase-front propagation by allowing material in each finite-difference cell to melt, undercool, nucleate, and solidify under prescribed conditions. Calculations indicate possibilities for a wide variety of solidification behavior. The new model and selected results of calculations are discussed here and comparison with recent experimental data are made. 12 references, 7 figures