Grain-scale deformation of a bimineralic composite by normal-stress-driven grain-boundary diffusive mass-transfer has been modelled using diffusion-creep software that, for the first time, allows different diffusion coefficients for interphase boundaries and grain-boundaries as well as for different components. By selecting suitable coefficients we have obtained a fully coupled mechanical and mass-transfer numerical solution for the formation of fibrous pressure-shadows or strain fringes at the interface between a rigid object and a deforming rock matrix of different compositions. The model is two-dimensional and run in pure-shear velocity mode to a stretch ratio of 1.4. The first results are reported, which show dissolution and face-controlled antitaxial growth of a soluble, polycrystalline, calcite matrix at the interface with a circular and relatively insoluble pyrite object. The ratio of CaCO3 diffusion along calcite-pyrite versus calcite-calcite boundaries strongly influences the extent of pressure-shadow growth and the pattern of strains in the matrix. A low ratio produces little growth, significant perturbation, and deflection of total-strain axes around the pyrite. An intermediate ratio produces appreciable growth, little perturbation, and near-parallel total-strain axes. A high ratio produces larger pressure-shadows, and total-strain axes that bend in towards the pyrite as if it were a weak object. Sliding and rotation of matrix grains are also affected. These results differ fundamentally from purely physical models of ductile flow around a rigid object and demonstrate the influence of interface diffusional properties on the resulting behaviour. In particular, assumptions such as perturbation of the flow by the object, deflection of external foliation around pre-deformational porphyroblasts and relationships of pressure-shadow strain to bulk strain may need to be re-examined in the light of this finding.