Abstract: Numerical methods for geometric nonlinear problems are core topics in computational mechanics courses. This paper generalizes and expands the measurements of large deformation, extablishing a unified derivation and expression of the energy principles and the finite element solution formulations for geometric nonlinear problems. The reference configurations of the deformable body are distinguished as unknown equilibrium configurations and known equilibrium configurations. The relationships among key principles and formulations are clarified, including the virtual displacement principle, virtual power principle, and incremental virtual displacement principle, the total Lagrangian formulation and the updated Lagrangian formation, the solution strategies of linearization followed by element discretization and element discretization followed by linearization, and the constitutive equations with the total, incremental and rate variables. This paper provides a clear and uniform framework for energy principles and finite element solution formulations for the geometric nonlinear problems, facillitating teaching, learning, understanding, and practical application.