We derive a solution for drawdown and stream depletion for shallow aquifer penetration by a stream and hydraulic aquifer connection with the underlying source bed. This solution unifies and extends the results obtained by Theis, Glover and Balmer, Hantush and Jacob, Hantush, and Hunt. We show that both hydraulic stream-aquifer connection and hydrostratigraphic conditions determine Maximum Stream Depletion Rate, which is defined as a maximum fraction of the pumping rate supplied by the stream depletion.