Solid volume increases during the hydration of mantle rocks. The fluid pathways necessary to feed the reaction front with water can be filled by the low density reaction products. As a result, the reaction front dries out and the reaction stops at low reaction progress. This process of porosity clogging is generally predicted to dominate in reactive transport models, even when processes such as reaction-induced fracturing are considered. These predictions are not consistent with observations at mid-ocean ridges where dense mantle rocks can be completely replaced by low density serpentine minerals. To solve this issue, we develop a numerical model coupling reaction, fluid flow and deformation. High extents of reaction can only be achieved when considering that the increase in solid volume during reaction is accommodated through deformation rather than porosity clogging. The model can generate an overpressure that depends on the extent of reaction and on the boundary conditions. This overpressure induces viscoelastic compaction that limits the extent of the reaction. The serpentinisation rate is therefore controlled by the accommodation of volume change during reaction, and thus by deformation, either induced by the reaction itself or by tectonic processes.