Abstract: Energy Collocation Method (ECM) was advanced by the auther of this Paper in 1979—1980.This paper attempts to give a brief introduction to its fundamentals and applications.The method based on the variation principle and the quadrature formula of the numerical integration method.According to the Variation Principle and the quadrature formula (e.g.,Simpson, Gaussian),a computational scheme of Energy Collocation Method has been developed by the author of this paper.The main features of this method are higher accuracy and more economy in computer storage and time requ-irements.The toothed can easily be carried out on a computer.