We develop a linear viscous constitutive relationship for pressure solution constrained by models of deformed metasedimentary rocks and observations of exposed rocks from ancient subduction zones. We include pressure and temperature dependence on the solubility of silica in fluid by parameterizing a practical van't Hoff relationship. This general flow law is well suited for making predictions about interseismic behavior of subduction zones. We apply the flow law to Cascadia, where thermal structure, geometry, relative plate velocity, and Global Positioning System velocity field are well constrained. Results are consistent with the temperature conditions at which resolvable ductile strain is recorded in subducted mudstones (at depths near the updip limit of the seismogenic zone) and with relative plate motion accommodated completely by viscous deformation (at depths near the downdip limit of the seismogenic zone). The flow law also predicts the observed forearc tapering of slip rate deficit with depth.