The dispersion of a passive tracer in fluid flowing between a source and a sink in a Hele–Shaw geometry, characteristic of field scale flows in a layer or fracture, is considered. A combination of analytic and numerical techniques and complementary experimental measurements are employed, leading to a consistent picture. This dispersion process is found to be characterized by a power‐law decay in time of the tracer concentration, with an exponential cutoff at very long times, in strong contrast to the Gaussian behavior associated with the widely used quasi‐one‐dimensional (1‐D) models.