The rate of stream depletion caused by cyclic pumping from a well located in a connecting groundwater aquifer was studied. Equations were developed by applying superposition principles to analytical solutions for steady continuous pumping. Dimensionless plots based on these equations have been developed; one for dimensionless volume of stream depletion over a pumping cycle and another for maximum rate of stream depletion at a practical state of dynamic equilibrium. These plots provide a way to quickly determine the time at which a practical state of dynamic equilibrium is reached and the error in stream depletion rates produced by neglecting the nonuniform pumping rate within a pumping cycle. Analysis showed that the volume of stream depletion over a cycle ending at time t, is the same as the volume of stream depletion between the start of pumping and time t by a single period of pumping. Analysis also showed that under some circumstances, approximating the effects of cyclic pumping by a steady, continuous pumping at the equivalent cycle-average rate is not adequate.