Axisymmetric compression testing (ACT) stands as a pivotal experimental technique, widely embraced for its capacity to identify the plastic flow attributes inherent to diverse materials. However, the accuracy of the flow curve obtained from ACT can be significantly affected by errors introduced by the inevitable barrelling and foldover, which can lead to erroneous interpretation of deformation phenomena. The existing analytical and numerical solutions for estimating effective stress in ACT are first reviewed. A new closed‐form solution that is insensitive to friction and foldover is then presented. The solution is based on a multilayer model of the sample geometry, which considers the instantaneous barrelling of the sample. The multilayer solution is validated against a reference numerical solution and shows good agreement, even after a significant foldover. The results indicate that the proposed framework can significantly improve the accuracy of material flow characterization. This can be of significant value in the fields of material processing, manufacturing, and materials science.