In ltration by a pure matrix in the presence of preform deformation and partial matrix solidi cation is analyzed using a bounding approach for the preform rheology where solid metal is present. It is found, using parameters for the in ltration of short alumina ber preforms by aluminum, that the two bounds are close in comparison to other factors of uncertainty in the prediction of in ltration rate. Using this approach, preform compression is shown to exert a signi cant in uence on the in ltration rate for the system explored; in particular, the analysis shows the existence of an optimal value of applied pressure. Simpli cations in the analysis are also presented, which yield fairly accurate results while easing their computation signi cantly.