Exact analytical solutions of vacuum-sublimation in an initially partially filled, frozen, porous medium are developed by the similarity variable technique. The sublimation interface temperature, pressure and vapor concentration are obtained in addition to the position of the sublimation interface. Two theoretical models corresponding to the two-region model which allows for vapor transfer in both the frozen region and dried region and the one-region model accounting for vapor transfer in the dried region only are considered. The comparison between these two models and the effect of mass convection into the frozen region are studied. The results show the significant discrepancies in the interface positions predicted by these two models for some values of the important parameters.