The injection of pure liquid metal into a fibrous preform initially at a temperature below the melting point of the metal results in partial solidification of the metal as it contacts the fibers. If the infiltrating metal is superheated, continued infiltration remelts this solid metal at a sharp front which propagates through the fiber preform. Because the permeability of the remelted region is greater than that of the partially solidified region, there is a driving force for the remelted region to advance in an unstable manner. In the present work, the morphological stability of a simplified infiltration system (steady-state, unidirectional, adiabatic infiltration with a pure metal) is analyzed using linear stability analysis. The resulting analytical solution illustrates the relationship between front stability and relevant processing parameters. The practical result of the derivation is that a stable remelting front can be maintained by keeping the infiltration velocity below a certain critical value.