This report is written to provide a background to the theory of geometric non-linearity and how finite element analysis deals with such non-linearities through a specially selected set of benchmarks. 

A theoretical background to geometric non-linearities is presented with emphasis on practical applications. 

Practical examples are used to demonstrate important features of non-linear geometric behaviour such as bifurcation and snap-through. A number of two-dimensional and three-dimensional geometric non-linearity FE benchmarks are presented with discussions of their attributes and reference solutions.