In the present work, a previously developed neural network approach for analyzing spherical indentation experiments is applied to prestressed specimens to determine the effect of residual stresses on the identified stress-strain curves. Within this scope, a comparison to other measurement errors has been made, which are caused by surface preparation and anisotropy of the material. To validate the experimental and analysis approach, the effect of compressive and tensile prestresses was also simulated using a three-dimensional finite element model. The material investigated is a rolled 2024 T351, which is widely used for manufacturing airplanes. It is shown that the existing neural network approach is able to determine the stress-strain behavior in agreement with that obtained from tensile tests. The method is robust against most error sources, such as surface roughness, coarse grain structure, and anisotropy, if a sufficient number of experiments are available. The most important influencing factor can be the residual stress causing errors up to 20% in the identified stress-strain curves.