Polycrystalline aggregates which contain some liquid in grain interfaces can deform by matter transport, through the liquid phase. If the applied stress is multiaxial, then the deviatoric component of the stress will produce creep, that is, a change in shape of the aggregate without any change in volume, while the mean stress will cause the aggregate to densify. Constitutive equations for creep rate and densification rate are derived. It is shown that the rate may be controlled either by the interface kinetics of dissoultion/precipitation of the crystal from the liquid or by the diffusion rate of matter through the liquid. The first process can be related to the kinetics of crystal growth from solution, and the second, to the visocisity of the liquid. The results of the analysis are used to interpret experiments on densification rate of a rock salt polycrystalline aggregate immersed in saturated brine.