The Ball-on-Three-Balls-test has proven to be an accurate and easy-to-use option for strength testing. However, the maximum stress must be calculated based on Finite-Element-Analysis results. For this purpose, a fitted function was already provided. This function is based on results which were generated under the assumption of punctiform load introduction. Deviations from these conditions occur through an increase in contact-area between the loading ball and the specimen, large specimen deformations, friction, or plastic deformation of the balls. These non-linear effects are investigated by Finite-Element-Analysis for a wide range of specimens. It is shown that the maximum stress is sensitive to the area of contact between the loading ball and the specimen. Furthermore, thin specimens are subject to large deformations, which significantly decrease the maximum stress. Therefore, a revised fitted function is derived. For specimens with exceptional geometries, non-linear effects are considered with correction factors added to the new fitted function.