<p>Pyramidal trusses, prized for their inherent geometric rigidity, high strength-to-weight ratio, and efficient load distribution, are becoming increasingly crucial across diverse engineering disciplines, including aerospace, mechanical engineering, and energy absorption systems. Recent progress in additive manufacturing and 3D printing has further broadened their utility in creating lightweight, high-performance structures, especially within the aerospace sector. This paper offers a thorough analysis of truss instabilities by employing the Green–Lagrange strain tensor, integrating both analytical and numerical methods to assess local buckling, length imperfections, geometric imperfections, and material plasticity. A novel technique, leveraging the determinant and eigenvalues of the tangent stiffness matrix, is introduced to accurately pinpoint critical points along the primary equilibrium path. The study underscores the significant impact of geometric and length imperfections, as well as plasticity and Euler buckling, on equilibrium paths and overall stability, effectively demonstrating how these factors affect the truss’s structural performance. In conclusion, this research enhances the structural analysis of pyramidal trusses, providing valuable insights for their design and implementation in contemporary engineering applications.</p>