Cratons are areas of continental lithosphere that exhibit long-term stability against deformation. Seismic evidence suggests that cratonic lithosphere may have formed via thrust stacking of proto-cratonic lithosphere. We conducted numerical simulations and scaling analysis to test this hypothesis, as well as to elucidate mechanisms for stabilization. We found that formation of cratonic lithosphere via thrust stacking is most viable for buoyant and viscous lithosphere that is thin and/or possesses low effective friction coefficients. These conditions lead to low integrated yield strength within proto-cratonic lithosphere that allows it to fail in response to convection-generated stresses. Specifically, formation via thrust stacking is viable for lithosphere with chemical to thermal buoyancy ratios of B = 0.75-1.5, viscosity contrasts between the lithosphere and convective mantle of Delta eta > 10(2), and friction coefficients of mu = 0.05-0.1. Preservation depends on the balance between the chemical lithosphere's integrated yield and convection-generated stresses. The physical process of thrust stacking generates a thickened cratonic root. This provides a higher integrated yield stress within cratons, which is more conducive to stability subsequent to formation. Increased friction coefficient values, due to dehydration, can also provide higher integrated yield stresses within cratons. To provide long-term stability, integrated yield stresses must be great enough to offset future mantle convection-generated stresses, which can increase with time as the mantle viscosity increases due to cooling. Thin or rehydrated cratonic lithosphere may not provide stability against the increasing convective stresses, thus providing an explanation as to why some cratons are not long-lived.