Upwelling in the Gulf of Mexico and along the coast of California has been treated theoretically by Hidaka for steady‐state conditions. An extension of this work is presented which considers the transient state in which upwelling and coastal currents gradually develop in an ocean initially at rest when the wind suddenly begins to blow over the sea surface. Expressions for the component velocity in thexandydirections, for the vertical component, and for the vortieity in the direction of the z axis are derived. A numerical example is included using the expression derived for thexcomponent of the curre