This paper discusses the limitations of extension of classical Hamiltonian Principle to continuous systems, then reviews the new developments of operational theory in functional analysis and variational principles in non equilibrium thermodynamics based on field variation. Complementary dual variational principles including adjoined variational methods and generalized Green function method are bases of finite element analysis and boundary element analysis as well. From the point of view of physics, variational principles of macroscopic non equilibrium thermodynamic can be applied to all continuous mechanical systems. However, they have some limitations in application scope and remain to be developed.