ABSTRACT The finite element method (FEM) is used widely in analysis of elasto-plastic behaviours for structures. The analysis often involves a two-stage process: first, the internal force field acting on the structural material must be defined, and second, the response of the material to that force field must be determined. In other words, the analysis of behaviours of structural material is establishment relationships between stresses and strains in the structure in the plastic as well as elastic ranges. It furnishes more realistic estimates of load-carrying capacities of structures and provides a better understanding of the reaction of the structural elements to the forces induced in the material. An understanding of the role of the relevant mechanical variables that define the characteristic reaction of the material to the applied force is therefore essential to the engineer designing structures. A complete account of the theory and application of plasticity must deal with two equally important aspects: (1) the general technique used in the development of stress-strain relationships for inviscid elasto-plastic materials with work hardening as well as strain softening; and (2) the general numerical solution procedure for solving an elasto-plastic structural problem under the action of loads or displacements, each of which varies in a specified manner.