Observations of seismicity and seismic tomography provide a present‐day constraint on the geometry of slabs within the mantle. However, it is challenging to directly relate the observed shape of slabs to their time evolution. Phase transitions modify the buoyancy forces within slabs, affecting how slabs deform as they sink into the lower mantle and how forces are transmitted to the surface plates. Here we show that if the crustal shear zone is sufficiently weak (1020 Pa s), then the coupled effects of a compositionally dependent phase transition model and a stress‐dependent rheology lead to oscillatory plate speeds and trench motion in response to buckling and folding of the slab. On average, subducting plate velocity is 4 cm/yr and trench motion is ±0.7 cm/yr. However, during folding, subducting plate speed and trench motion increases by a factor of 3 and trench motion switches from advance to retreat. In models with a higher‐viscosity shear zone (1021 Pa s), average plate speed is lower (2 cm/yr) and there is only trench advance. Stress‐dependent weakening due to increasing driving stresses can also cause unexpected changes in plate velocity (i.e., decrease or no change). In addition, due to the added negative buoyancy from the phase transitions, slab breakoff occurs in models with a yield stress ≤500 MPa. Because of the oscillatory motion of the trench, long flat slabs do not form in the transition zone: this suggests that other factors, such as interaction of the slab with deep mantle flow, may be required to create long flat slabs.