This paper reviews and compares finite element formulations for non-linear static and dynamic analysis, focusing on large displacements, strains, and material non-linearities. The formulations are based on continuum mechanics principles and are used to solve problems involving elastic, hyperelastic (rubber-like), and hypoelastic materials. The paper discusses two main formulations: the total Lagrangian (T.L.) and updated Lagrangian (U.L.) formulations. The T.L. formulation refers all variables to the initial configuration, while the U.L. formulation refers them to the current configuration. Both formulations are used to derive the equilibrium equations for the body, which are then solved using isoparametric finite element discretization. The paper also discusses the numerical solution of these equations, including the calculation of stress-strain matrices and the use of constitutive relations for elastic and hyperelastic materials. The paper concludes that the choice of formulation depends on the numerical effectiveness of the method, and that both formulations can yield identical results if the material tensors are appropriately related. The paper also presents a detailed derivation of the equilibrium equations for both formulations and discusses the numerical efficiency of each. The paper also includes a summary of the step-by-step integration algorithm used in the finite element analysis.This paper reviews and compares finite element formulations for non-linear static and dynamic analysis, focusing on large displacements, strains, and material non-linearities. The formulations are based on continuum mechanics principles and are used to solve problems involving elastic, hyperelastic (rubber-like), and hypoelastic materials. The paper discusses two main formulations: the total Lagrangian (T.L.) and updated Lagrangian (U.L.) formulations. The T.L. formulation refers all variables to the initial configuration, while the U.L. formulation refers them to the current configuration. Both formulations are used to derive the equilibrium equations for the body, which are then solved using isoparametric finite element discretization. The paper also discusses the numerical solution of these equations, including the calculation of stress-strain matrices and the use of constitutive relations for elastic and hyperelastic materials. The paper concludes that the choice of formulation depends on the numerical effectiveness of the method, and that both formulations can yield identical results if the material tensors are appropriately related. The paper also presents a detailed derivation of the equilibrium equations for both formulations and discusses the numerical efficiency of each. The paper also includes a summary of the step-by-step integration algorithm used in the finite element analysis.