The theoretical framework for modeling pressure solution in polyphase rocks is presented. It is often assumed that pressure solution is a deformation mechanism of secondary importance deep in the lithosphere. It is shown here that the rheology of rock during pressure solution may be drastically reduced in a bimineralic and polymineralic rock relative to its monomineralic counterparts, and therefore the importance of this deformation mechanism importance is perhaps underestimated. This behavior contrasts with that of a polymineralic rock undergoing dislocation creep, where existing models show that the rheology will be some average of the rheologies of individual phases. For instance, the rheology of a dunite in pressure solution is governed by the diffusion of both MgO and SiO2; whichever is the slowest will control the viscosity of the rock. Conversely, in a harzburgite with a specific texture, flow will be governed by the fastest diffusing species; thus its strength may be as low as that of a quartz rock of comparable grain size. Given the comparative strength of many phases undergoing dislocation creep relative to quartz, this prediction implies a larger range of conditions under which pressure solution forms an important part of bulk rock deformation than inferred previously. Predictions on textural evolution of polymineralic aggregates are also made, and it is shown that some minerals grains may become elongate parallel to the maximum principal stress during deformation, even though the rock as a whole shortens in this direction. ¿ American Geophysical Union 1992