This book presents a unified computational approach to postbuckling stability analysis of structures using the Total Potential Energy (TPE) framework. It builds upon the secant matrix technique (N1-N2 method) and introduces the Variable Order Secant Matrix (VoSM) method, providing a robust framework for analyzing reticulated, framed, continuum, and thin-walled systems under large deformations. The book derives the geometric nonlinear finite element formulations using Total Lagrangian (TL) and co-rotational TL formats, ensuring accurate postbuckling analysis. It includes benchmark problems and numerical case studies, making it a valuable resource for graduate students, researchers, and faculty involved in structural stability and advanced postbuckling investigations. Additionally, it serves as an indispensable reference for analyzing and designing steel structures.