A one-dimensional (1D) flow, resulting from a sudden rise or decline in the water stage of a flood channel in a composite aquifer, which consists of two different regions separated by a linear discontinuity parallel to the channel, is considered. Governing equations are solved analytically for appropriate initial and boundary conditions. The obtained solution allows the determination of water level fluctuations in both regions of the composite aquifer and the time-dependent flow rate to (or from) the aquifer. It is shown that three other solutions found in the literature (solutions for uniform finite aquifer with impervious boundary, uniform finite aquifer with recharge boundary, and uniform semiinfinite aquifer) are special cases of the proposed solution, and they are unified in one form. The proposed solution is a relatively simple means of predicting the variations in the water levels in the aquifer as well as evaluating the time-dependent flow rate. It may also be used for the identification of the aquifer properties and for numerical model validation.