The method of vertical mode expansions for inviscid time-dependent motions is simple and well known (see Gill, 1982). The method simplifies the description of three-dimensional stratified circulation by representing each circulation variable as a series expansion of orthogonal functions of z (the vertical coordinate). Several papers, for example, McCreary (1981) and McCreary and Chao (1985), have represented wind-forced coastal upwelling in terms of such inviscid modes, even when the circulation is viscous. By using the inviscid modes, however, these papers were unable to represent the sea surface density anomaly produced by the wind stress. Instead of persisting with the vertical modes of the inviscid system, this paper derives new viscous vertical modes which have the advantage of allowing nonzero surface density anomalies, produced by the vertical diffusion of density anomalies below the surface. ¿1991 American Geophysical Union