The effects of kinetics on the non‐equilibrium aspects of the olivine to spinel transition in a descending slab have been studied numerically. A one‐dimensional model consisting of the kinetic equations and the heat‐diffusion equation with latent‐heat release has been constructed. Numerical results show that the position and sharpness of the kinetic phase boundary is determined by the surface tension and the activation volume. For slow slab velocities, less than 6 cm/yr, near equilibrium conditions are found. Finger‐like structures emanating from the phase boundaries are obtained in this regime. These phase boundary prolusions may cause earthquakes. For slab velocities of around 10 cm/yr the metastable olivine region may be pushed down to a depth of about 600 km, with a sharp phase boundary. A direct transition from olivine to perovskite may be feasible.