Of all mass, momentum, and energy sources and sinks in simulating the feed, withdrawals, and scoops in the flow field of a gas centrifuge by using Onsager's pancake equation, the most complicated ones are mass sources/sinks, which impose very different boundary conditions from those by other sources/sinks. Therefore, so far an analytical solution has not been found for the flow field with a mass source/sink. Here a solution procedure is described in detail for solving the flow field in the presence of a mass source/sink, and an analytical solution is given. Numerical examples are also presented and analyzed.