The interactions between reactive fluids and solids are critical in Earth dynamics. Implications of such processes are wide ranging: from earthquake physics to geologic carbon sequestration and the cycling of fluids and volatiles through subduction zones. Peridotite alteration is a common feature in many of these processes, which—despite its obvious importance—is relatively poorly understood from a geodynamical perspective. In particular, although frequently observed in nature, it is still unknown how rocks can undergo 100% hydration/carbonation. One potential explanation of this observation is the mechanism of reaction‐driven cracking: that volume changes associated with these reactions are large enough to fracture the surrounding rock, leading to a positive feedback where new reactive surfaces are exposed and fluid pathways are created. The purpose of this study is to investigate the relative roles of reaction, elastic stresses, and surface tension in alteration reactions. In this regard, we derive a system of equations describing reactive fluid flow in elastically deformable porous media, which we apply to a model of serpentinization in a subseafloor environment. The stoichiometry of the serpentinization reaction predicts net volume reduction of the multiphase system, which, according to our numerical simulations, can lead to failure in tension. We also explore a parameterization of surface energy in the model, which allows fluid to infiltrate regions of dry peridotite, significantly changing the stresses and potentially leading to growing crack fronts.