One of the prevalent challenges in the design, numerical analysis and verification of structural membranes lies in the non-linearity of their load-response curves. Structural analysis has to be performed with a geometrically non-linear approach, due to the interaction of form and forces and thus a linear extrapolation or combination of analyis results is not possible. The appropriate modeling of the environmental impacts (such as wind and snow) also has a significant influence on the analysis results. Furthermore, non-linear material behavior can be of interest. The resulting load-response curves (e.g. stresses, deformations) are typically non-linear and their interpretation towards the underlying safety requirements is not straight forward. In addition, the prestress also has a major influence on membranes' structural behavior. However, the current European regulations for the proof of the limit states (ULS and SLS) of any building requires a simplified categorization of the structural behavior. This research investigates the load-bearing behavior of typical re-occurring membrane shapes in the context of current verification requirements. Typical load cases are applied and the structural behavior is shown under consideration of the mentioned non-linearities.