Serpentinite subduction and the associated formation of dehydration veins is important for subduction zone dynamics and water cycling. Field observations suggest that en-échelon olivine veins in serpentinite mylonites formed by dehydration during simultaneous shearing of ductile serpentinite. Here, we test a hypothesis of shear-driven formation of dehydration veins with a two-dimensional hydro-mechanical-chemical numerical model. We consider the reaction antigorite + brucite = forsterite + water. Shearing is viscous and the shear viscosity decreases exponentially with porosity. The total and fluid pressures are initially homogeneous and in the antigorite stability field. Initial perturbations in porosity, and hence viscosity, cause fluid pressure perturbations. Dehydration nucleates where the fluid pressure decreases locally below the thermodynamic pressure defining the reaction boundary. Dehydration veins grow during progressive simple-shearing in a direction parallel to the maximum principal stress, without involving fracturing. The porosity evolution associated with dehydration reactions is controlled to approximately equal parts by three mechanisms: volumetric deformation, solid density variation and reactive mass transfer. The temporal evolution of dehydration veins is controlled by three characteristic time scales for shearing, mineral-reaction kinetics and fluid-pressure diffusion. The modelled vein formation is self-limiting and slows down due to fluid flow decreasing fluid pressure gradients. Mineral-reaction kinetics must be significantly faster than fluid-pressure diffusion to generate forsterite during vein formation. The self-limiting feature can explain the natural observation of many, small olivine veins and the absence of few, large veins. We further discuss implications for transient weakening during metamorphism and episodic tremor and slow-slip in subduction zones.