A one-dimensional shear flow model of the upper mantel beneath continents is presented. The model includes a two-layer crust with values of thermal conductivity and radiogenic heat production distinct from those of the underlying mantle, in which the conductivity is generally a function of temperature and depth. Temperature, velocity, effective viscosity, and volumetric heat generation profiles are determined, accounting for viscious dissipation and using a temperature and pressure dependent nonlinear mantle rheology in which the rate of strain is directly proportional to a power n of the shear stress (n=3 is generally assumed, although the Newtonian case is investigated). The solutions provide the values of lower crustal radiogenic heat production and shear stress, which are a priori unknown. The boundary conditions on the model are the values of velocity, temperature, and heat flux at the surface and the vanishing of velocity with a prescribed upward heat flux at great depth. The models produce a shear zone (asthenosphere), the region where the geotherm bends over, the velocity drops rapidly to zero, the viscosity has a minimum value, and the shear stress heating has a maximum value. The thickness and depth of the shear zone, the value of viscosity therein, the associated shear stress, the lower crustal radioactivity, and other characteristics of the model depend on parameters such as the activation energy and volume of the constitutive stress-rate of strain equation, plate velocity, mantle radioactivity, and heat influx from the lower mantle. These dependences are explicitly demonstrated through the presentation of a series of numerical calculations. A realistic model of the mantle beneath stable continental regions is found which satisfies the additional constraints of the temperature at and the depth to the shear zone inferred from the petrology of peridotite xenoliths in kimberlites from South Africa, the seismic shear wave structure beneath shields, and the value of radioactivity in gabbroic rocks likely to represent the lower crust. The activation volume V* is the most important constitutive parameter controlling the depth of the shear zone. The model for stable continent regions predicts that V* is perhaps twice as large as would be appropriate for diffusion of O-- ions. Viscous dissipation contributes about 0.1 HFU (μcal cm-2 s-1) to the continental surface heat flux. Through thermal feedback as a result of the pressure and temperature dependence of the viscosity, shear stress heating leads to the formation of an asthenosphere decoupling the plates from the underlying mantle.