One of the models proposed for mantle convection is a counterflow in the asthenosphere to balance the motion of the lithospheric plates. An analysis of this hypothesis has been made, using a model in which the variables depend only on depth. Velocity and temperature profiles are coupled by a temperature- and depth-dependent viscosity. The velocity of the crustal plate and the actual viscosity function are the only inputs to the model. Pressure must increase with distance from the ridge for there to be a return flow at depth and no net mass flow across a vertical section. Horizontal pressure gradients between about 0.1 and 1.0 b/km and shear stresses at the crustal plate between 0.1 and 0.4 kb have been obtained for wide variations in the plate velocity and the viscosity function. However, for these same examples, the surface heat flux is remarkably insensitive to parameter variations; it is between about 0.2 and 0.3 μcal/cm² sec. Heating by viscous dissipation provides a self-lubricating mechanism. The higher the plate speed, the lower is the drag on the plate.