We discuss a measurement method that aims to determine the radial distribution of the photoelastic constant C in an optical fiber. This method uses the measurement of the retardance profile of a transversely illuminated fiber as a function of applied tensile load and requires the computation of the inverse Abel transform of this retardance profile. We focus on the influence of the measurement error on the obtained values for C. The results suggest that C may not be constant across the fiber and that the mean absolute value of C is slightly larger for glass fibers than for bulk fused silica. This can, for example, influence the accuracy with which one is able to predict the response of optical fiber sensors used for measuring mechanical loads.