The objective of this study is to apply the combined linear buckling and nonlinear analysis to the stability investigations of the plane and space frame structures. A comparative study of the combined analysis and the nonlinear analysis is conducted with ABAQUS to demonstrate the applicability and effectiveness of the combined analysis for the critical load predictions. Several test problems and a glulam dome cap are analyzed, and the critical load prediction curves and the nonlinear equilibrium paths are presented. It is verified that the B33 finite element in ABAQUS is capable of modeling the curved beam. The modeling procedure of the dome cap model is discussed. Finally, conclusions and recommendations are made for future studies.