Typical problem areas of interest include structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The analytical solution of these problems generally requires the solution to boundary value problems for partial differential equations. In particular, the focus will be on the Finite Element Method and its application to linear and nonlinear problems. Aim of the present proposal is to: initiate the investigation on the Universal Matrix method which is introduced presently for linear elastic and transient heat transfer problems when applied to non-linear elastic and inelastic problems. Multiple databases are searched for literature and limiting to last ten years. The keywords selected for the search were a combination of the nonlinear heat transient, inelastic problems. Universal Matrix Method applied to nonlinear heat transient & inelastic problems which a time is reducing than the existing methods like Gauss Quadrature methods, etc. Research on usage of various methods other than Gauss Quadrature method applied to linear problems extended to nonlinear heat transient & inelastic problems.