Three-dimensional numerical models are presented for thermal convection of non-Newtonian fluid with viscosity that depends on temperature and stress to understand development of moving plates on the Earth. A hysteresis is assumed in the relationship between stress and viscosity to make the viscosity depend on stress-history. The stress-history dependence due to hysteresis induces a regime where plates or highly viscous pieces of lithosphere separated by narrow and mechanically weak plate margins rigidly move by their own weight. The plate margins newly develop when a stress high enough to cause lithospheric rupture is induced in the lithosphere by the help of hot cylindrical uprising plumes but do not spontaneously develop by the weight of lithosphere itself. The high rupture strength of lithosphere makes the plate-like motion rather steady without the help of viscosity reduction by melting in the asthenosphere.