In this thesis, variable-node elements (VNEs) based on the cell-based smoothed finite element method (CSFEM) are proposed with emphasis on their applications for elasto-plastic finite deformation. The formulation of CSFEM is extended to cover elastic-plastic deformations beyond the classical linear theory of elasticity, which has been the major application domain of smoothed finite elements. The finite strain deformations are treated with the aid of the formulation based on the hyperelastic constitutive equation. The volumetric locking originating from the nearly incompressible behavior of elasto-plastic deformations is remedied by relaxing the volumetric strain through the mean value. In addition, the existing VNEs limited to linear elastic analysis is extended to analysis of elasto-plastic deformations with the aid of CSFEM. The comparison with the conventional finite elements and Abaqus demonstrates the effectiveness and accuracy of the present approach.