Flow birefringence has become increasingly popular as a tool in non‐Newtonian fluid mechanics, where it provides a means of measuring stress distributions in complex polymer flows. In order to access a wider range of kinematic complexity in the testing of constitutive models, we explore the application of flow birefringence in axisymmetric geometries. Unlike traditional applications of flow birefringence in two‐dimensional flows, there is no direct relationship between measured optical properties and stresses in the material. Rather, the optical properties reflect the cumulative effect of the axisymmetric refractive index (and hence stress) tensor on the polarization state of light. Since a typical goal of flow birefringence studies is comparison between experiment and computation, we propose that optical property distributions could serve as the basis for comparison rather than attempting to invert optical data to yield radial stress distributions. In the limit of small total retardance, there are particularly simple relationships between experimental observables and integrals of the stress distributions. Experiments are performed on an index‐matched Newtonian test fluid in a prototype axisymmetric geometry (tube flow past an obstruction with a hemispherical cap) in order to illustrate the principles of the technique.