A kinetic model for analyzing phase front propagation during freezing of a fine porous medium under conditions of moisture diffusion is presented. Crystallization is assumed to take place in a kinetic zone according to an experimental function characterizing the crystallization rate. The method was demonstrated for the crystallization of a 1-D fine-grained soil medium subject to constant boundary conditions. The numerical results were validated against experimental data from the literature. The following conclusions were inferred from the theoretical results : (1) in a closed system the rate of phase front propagation can oscillate even under constant boundary conditions; (2) as the phase front reaches a stationary state, the diffusional moisture dux from the non-frozen zone to the kinetic zone vanishes.