A thick-walled cylindrical specimen containing an external circumferential groove was subjected to external pressure. To investigate the maximum pressure sustainable by the reduced wall thickness, strain gage measurements were taken during external pressurization tests. For comparison to experimental results, an elastic-plastic notch stress-strain analysis was conducted based on Neuber’s rule. The analysis utilized multiaxial elastic finite element results along with elastic-plastic tensile test data for the cylinder material. Based on experimental observations, it was necessary to supplement the approach with an additional relation between elastic and elastic-plastic multiaxial strains for the axisymmetric geometry under investigation. Assuming an invariant hoop to radial strain ratio rather than an invariant hoop to axial strain ratio provided better agreement with experimental results. It is demonstrated that the boundary conditions used to model the specimen had a substantial effect on the finite element results, even though the boundary was somewhat removed from the region of concentrated stress. Biaxial strain measurements are presented versus pressure over the elastic and into the plastic regime, and deformation plasticity theory was used to compute stress and radial strain components corresponding to measured strains. It is demonstrated that in order to apply a multiaxial Neuber’s rule to accurately estimate the elastic-plastic stress-strain response (using elastic stress concentration information and elastic-plastic material data), it is necessary to utilize an experimental observation that the ratio of the hoop to radial strain remains invariant from the elastic to the elastic-plastic regime. This differs from published assumptions about invariant hoop-to-axial strain ratios based on analysis of circumferentially grooved solid shafts. The predictions are accurate for moderate plastic strains, but correlation breaks down for bulk plastic deformation.