Archean cratons are the most stable tectonic units and their lithospheric mantle is chemically depleted and buoyant relative to the underlying mantle. The chemical depletion leads to high viscosity that maintains the long-term stability of cratons. However, the eastern part of the North China Craton ($1200 km in horizontal length scale) had been extensively reactivated and modified over a time scale of $100 Myr in the Mesozoic and Cenozoic. While the causes for the weakening of the North China Craton, a necessary condition for its reactivation, are still in debate, we investigate gravitational instability of compositionally buoyant lithosphere, by computing 2-D thermochemical convection models with different buoyancy number, lithospheric viscosity, and rheology. We find that the gravitational instability of cratonic lithosphere can happen over a larger range of buoyancy numbers with non-Newtonian rheology, but lithospheric instability with Newtonian rheology only happens with relatively small buoyancy numbers. For cratonic lithosphere with non-Newtonian rheology and relatively weak temperature-dependent viscosity, the instability starts in the cold, shallow part of the lithosphere and has small horizontal length scale (<300 km), leading to efficient thermal and chemical mixing with the underlying mantle. For cratonic lithosphere such as the eastern North China Craton, the instability process is episodic and consists of multiple instability events that may last for $100 Myr. The instability process revealed from our study explains the observations of episodic magmatism/volcanism events, geochemical mixing, and time scales associated with the reactivation of the North China Craton.