Nonlinear numerical models of continuously stratified seas are developed for vertical sections to study the mechanism of coastal upwelling and coastal jets in two kinds of seas: the so-called finite or closed sea bounded by two vertical coastal coasts

without elevation of sea surface

but with a flat bottom; and the semi-infinite sea bounded by only one vertical coast

with both an elevation of sea surface and a flat or inclined bottom. Constant wind stress in the first case

and constant wind stress or negative wind stress curl in the second case

are abruptly imposed. The key procedure for the mathematical analysis is to calculate the horizontal pressure gradient first by a special treatment. In the first case

the variation of horizontal components of velocity is changed with time to show three successive time intervals. The results show that the width of baroclinic jets depends upon (σS)1/2

and that distribution of isopycnic lines delineates the warm and cold regions. The relative importance of each term in the equilibrium among forces is thus determined. Distribution of stream function in vertical section reveals the upper and bottom Ekman layers. Two coastal jets are found with different alongshore velocities. The distribution of density anomalies displays the horizontal diffusion adjustment. An unstable case appears at different surface boundary conditions. In the second case

the vertical velocity will be stronger in the sea with less stratification

with an inclined bottom

and with a negative wind stress curl. The horizonatal offshore velocity increases in strength in a sea with inclined bottom and with negative wind stress curl. The vertical circulation pattern reveals the upwelling only. The distribution of density shows the isopycnic lines lifted upward near the shores. Obviously

the range of elevation of sea surface near the shore is larger than that far offshore. The jet width is less than the Rossby radius of deformation. A stronger jet will occur in more shallow water with negative wind stress curl. The coastal jet does not develop when the coefficient of horizontal turbulence increases to a certain limiting value.