A coupled thermal and mechanical solid state model of the oceanic lithosphere and asthenosphre is presented, which includes vertical conduction of heat with a temperature-dependent thermal conductivity k(T), horizontal and vertical advection of heat, viscous dissipation of shear heating, and linear or nonlinear deformation mechanisms with temperature- and pressure-dependent constitutive relations between shear stress and strain rate. A priori assumptions and inputs to the model are relatively few. The model determines the depth- and age-dependent temperature, horizontal and vertical velocity, and viscosity structures of the lithosphere and asthenosphere. Ocean floor topography, oceanic heat flow, and lithosphere thickness can be deduced as functions of the age of the ocean floor. The model also yields the age-dependent shear stress in the lithosphere and anthenosphere. Seismic velocity profiles are constructed which exhibit a marked low-velocity zone.