New solutions in the Laplace and time domains are developed that describe the transient response of a leaky aquifer to constant and transient discharge into a fully or partially penetrating sink with storage, A parameter estimation procedure based on the Newton-Raphson algorithm is found to be robust in a synthetic example involving a pumping test of a large-diameter well situated in a leaky strip aquifer. The analytical solutions presented may find applications in describing water movement in strip aquifers, in aquifers discharging into channels or streams, or in thin laboratory tanks.