FINITE ELEMENT METHOD AND ITS APPLICATIONS discusses the methods in a general frame and the performance on the computer, the variational formulations for elliptic boundary value problems, the error estimates and convergence for finite element approximate solutions and nonstandard finite element. In particular, presentations of the subject include the applications of finite element method to various scientific and engineering problems, for example, three dimensional elastic beam, elastic mechanics, three dimensional neutron diffusion problems, magneto hydrodynamics, three dimensional turbomachinery flows, Navier-Stokes equations and bifurcation phenomena for nonlinear problem, etc. Most applications results were established by the authors in the past three decades.