A linear stability analysis is performed for two‐ and three‐dimensional steady source and sink flows. Cases studied include inviscid compressible and incompressible fluids. For two‐dimensional flows viscous incompressible fluid is also examined. The one‐dimensional nature of the unperturbed base flow suggested taking the vorticity as a perturbation in order to reduce the number of variables and to simplify the analysis. It is shown that source flows are always unstable. Sink flows are found unstable for inviscid compressible fluid and also for two‐dimensional flow of viscous incompressible fluid for low Reynolds numbers. The different modes of instability existing in perturbed flow are obtained. ©1995 American Institute of Physics.