Two prominent continuum mechanics based incremental nonlinear finite element formulations are reviewed. An introduction to different material response measures suitable for nonlinear analysis, in addition to an overview of the Total and Updated Lagrangian reference frames, serve as the starting point for this review. The two nonlinear formulations are specialized for use with a geometrically nonlinear plane truss finite element. The truss formulations are then implemented into separate geometrically nonlinear finite element codes. Numerical comparisons of five test structures are carried out using ABAQUS and both programs. ABAQUS serves as the bench-mark by which the solution accuracy of the two programs is judged. / Master of Science / incomplete_metadata