The linear, stratified ocean model of McCreary (1981) is used to study the wind-driven response of the ocean near an eastern coast. The model can be regarded as an extension of the inviscid models of Lighthill (1969) and of Gill & Clarke (1974) that allows the vertical diffusion of heat and momentum into the deep ocean. Solutions are still found as expansions of vertical normal modes. Vertical mixing affects each mode as a linear drag with a drag coefficient that increases rapidly with mode-number, n. A zonally uniform band of steady equatorward winds forces the ocean, and the resulting flow field has many features in common with observations at eastern boundaries. There is a surface equatorward jet and a poleward Coastal Undercurrent confined within 10-20 km of the coast. Both currents extend well poleward of the wind band. Upwelling does not reach great depths, but occurs only above the core of the Undercurrent. Weak downwelling occurs at greater depths. There is offshore Ekman drift in the surface mixed layer and return flow at a depth slightly above the core of the Undercurrent. The baroclinic alongshore pressure gradient field and the vertical mixing of heat and momentum are essential elements of the model dynamics, but the $\beta $ and horizontal mixing are not. Low-order vertical modes (n < 6) tend to adjust to Sverdrup balance by the radiation of Kelvin and Rossby waves. These modes establish the alongshore pressure gradient field. High-order modes (n > 6) tend toward a two-dimensional balance. They generate the transverse circulation pattern associated with coastal Ekman pumping.