The overall compaction of porous rocks due to intergranular pressure solution (IPS) results from the dissolution of minerals within contact regions and the diffusive transport through the grain boundary of the dissolved species towards the fluid-filled pore space. The grain boundary structure can be imagined to be composed of dry contact zones, thin fluid films and fluid-filled cavities. The connectiveness and tortuosity of this structure determine the effective diffusivity of grain contacts and thus the potential of porous rock to compact by the action of IPS. The evolution in time of the grain-boundary structure, and thus of the effective diffusivity, is discussed here with the help of two 2D initial- and boundary-value problems which are solved by analytical and numerical means. The evolution of the solid–fluid interfaces within the grain boundary is governed by a phase transformation between the non-hydrostatically stressed elastic solid and the trapped fluid assumed in mechanical equilibrium. The characteristic time is provided by a linear kinetic law. The evolution of the structure away from a state of thermodynamic equilibrium during a loading normal to the grain boundary is found to occur in two steps. The first one consists of a diffuse morphology evolution in time and results in an enhancement of any initial stress concentration. The second step is characterized by a rapid and localized dissolution in the region of stress concentration. The latency period prior to localization is governed by the magnitude of the non-hydrostatic remote stress as well as the microstructural geometric factor responsible for the initial stress concentration at the solid–fluid interface. The localized dissolution is shown to provide a mechanism for the fluid to penetrate a previously dry contact region by marginal dissolution and thus to create a fluid film. However, the newly formed thin fluid layer is found to be unstable pointing to a possible repeated reorganization or dynamic evolution of the grain boundary internal structure during the action of IPS.