This paper describes a numerical study of the effect of vibration on two materials processes characterized by coupled transport-reaction phenomena. The first process is the production of SiC by the infiltration of porous carbon preform with molten silicon or silicon alloy, and subsequent chemical reaction between Si and C. The second process involves the burnout of organic binders from ceramic greenware. Transport equations are solved by the finite-domain numerical scheme for the conservation of mass, momentum, energy and species concentration in the porous media. A simple harmonic vibration is imposed as a transient source on the momentum equations. The growth rate of SiC and pressure rise in the ceramic greenware are predicted. The results demonstrate the potential of vibration to improve both materials processes. It is suggested that further systematic studies may allow the signatures of vibration to be used for characterization of the final products.