We present a coupled thermal and mechanical solid state model of the oceanic lithosphere and asthenosphere which includes vertical conduction of heat with a temperature-dependent thermal conductivity k (T), horizontal and vertical advection of heat, viscous dissipation or 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. We require a constant horizontal velocity u0 and temperature T0 at the surface and zero horizontal velocity and constant temperature T∝ at great depth. In addition to numerical values of the thermal and the depth- and age-dependent temperature, horizontal and vertical velocity, and viscosity structures of the lithosphere and asthenosphere. In particular, we deduce therefrom ocean floor topography, oceanic heat flow, and lithosphere thickness as functions of the age of th ocean floor. The model also yields the age-dependent shear stress in the lithosphere and asthenosphere. From the age-dependent geotherms and assumed values of the elastic parameters we construct seismic velocity profiles which exhibit a marked low-velocity zone. To a first approximation, simple boundary layer cooling, i.e., the growth of a cold thermal boundary layer by upward conduction of heat with k (T) and horizontal advection of heat with constant velocity u0, determines the thermal structure and quantities derivable essentially solely therefrom, namely, oceanic heat flow, ocean floor topography, and seismic velocities. The simple boundary layer cooling solution gives heat flow or ∝ (age)1/2 and depth of the ocean ∝ (age)1/2, for example. The second approximation, i.e., the self-consistent thermomechanical solution, provides modifications to the thermal structure associated with shear heating effects. This solution also gives the horizontal and vertical velocity and viscosity structures not determined by simple boundary layer cooling and such quantities as the age-dependent lithosphere and asthernosphere thicknesses derivable from the mechanical field. Effects of viscous dissipation at old ages tend to flatten heat flow, ocean depth, and lithosphere thickness versus age curves; e.g., although ocean depth and lithosphere thickness tend to increase with age at all ages, shear heating tends to reduce the rate of increase at old ages below that given by (age)1/2. The importance of shear heating increases with plate velocity, decreases with subasthenospheric temperature T∝, increases with the activation volume describing the pressure dependence of viscosity, and increases with age of the ocean floor.