The problem of a steady flow in the beta plane of an eastward vertically sheared stably stratified current over a shallow topography is formulated in the inviscid parameter regime, and a general governing equation and boundary conditions for the pressure field are obtained; conclusions are obtained only for an unsheared flow. For this case of an unsheared stably stratified eastward flow the mean motion and baroclinic motion may be decoupled, the mean motion obeying the barotropic vorticity equation. If the stratification is small, the baroclinic solution is obtained explicitly. The baroclinic motion has deeper water on the left near the bottom and deeper water on the right near the top in the northern hemisphere, and the opposite sense holds true for the southern hemisphere. Over a conical topography in the northern hemisphere the barotropic motion is clockwise; the baroclinic motion thus reinforces the barotropic motion near the bottom and opposes it near the top. For an unsheared current with a linear but not necessarily small stratification and an arbitrary bottom topography, an explicit solution for the flow is obtained as well as expression for the net forces exerted by the current on the topography. By using this general solution the specific example of a north-south ridge is computed in detail. This calculation confirms the general features of the baroclinic motion which were derived for small stratification.