Reactions in the Earth's crust occur through a dissolution-precipitation process in the presence of fluid. Dissolution releases aqueous species which are transported to the locus of precipitation. This replacement process generates creep deformation (i.e., dissolution-precipitation creep) due to volume change during reaction and stress-controlled mass re-distribution in the rock. Reaction under stress also modifies the rock microstructure and the pressure record during metamorphism. A quantitative model for dissolution-precipitation creep is developed here by considering both dissolution and precipitation at grain interfaces to simulate replacement reactions under stress. A new creep law is obtained for pressure solution, allowing for the reaction- and the diffusion-controlled cases to be modeled with a single expression. It is extended to replacement reactions by introducing volume change during reaction. Deformation mechanism maps are generated with the new creep law, indicating that, when fluid is present, dissolution-precipitation creep is the dominant deformation mechanism in the Earth's crust. Numerical model reveals that grain shape preferred orientation only develops near thermodynamic equilibrium. This is consistent with measurements of porphyroblasts preferred orientation in rocks from the Nufenen Pass (Switzerland) having experienced prograde metamorphism. Kinetics play a key role on the thermodynamic pressure of metamorphic reaction. Near the equilibrium, reaction is controlled by either σ1 or σ3 depending on the total volume change during reaction whereas it is controlled by the mean stress far from the equilibrium.