This is a study of numerical studies of three-dimensional mantle convection. The model includes lithospheric plates driven by body forces and basal tractions. The calculations will address a number of important questions bearing on the motion and evolution of lithospheric plates, and how they influence flow in the mantle. Problems include (1) studies of how the toroidal flow introduced by plate motions influences deformation and the rate of mixing in the mantle; (2) multiple plates interact with mantle convection, and the relation between individual plate motions and the underlying mantle flow; (3) studies of the stress induced in plates by mantle convection, and how changes in the forces on plates influences their deformation and the formation of new plate boundaries.