In this paper we exhibit analytical solutions for the upwelling and the coastal currents induced by periodic wind stress. We present solutions for an infinite deep ocean and for a shallow ocean. There is upwelling only when the period of the forcing is longer than the inertial period,i.e. f>ω. When the period of the forcing is shorter than the inertial period,i.e. f<ω, there is not upwelling, but propagating waves are excited.