An analysis of transient multidimensional solidification in the presence of a growing shrinkage cavity has been performed. The enthalpy model, which had previously been applied only for cases with no density change, has been extended to accommodate substances which undergo a change of density upon phase change. The extended enthalpy model was implemented by an efficient, implicit finite difference scheme. A solidification model was adopted in which the shrinkage cavity is at the top of the container within which the phase change is taking place. Solutions were carried out for solidification of a liquid in a long, horizontal rectangular container with convectively cooled walls. Results are presented for the time variations of various heat transfer quantities and for the evolution of the shrinkage cavity and the solid-liquid interface, for parametric values of the Biot number, liquid-solid density ratio, and Stefan number. The influence of the density ratio and the Stefan number on the heat transfer results was most marked at times near the completion of solidification, whereas the Biot number had a major effect at all times.