That the finite element method has become in recent years one of the most important methods used in computational mathematics, which has been used to solve complex engineering problems and finding solutions to scientific problems. It is a powerful and popular numerical method. In a partial solution Differential Equations (PDEs), with use in finding solutions by dealing with complex engineering fields and Various boundary conditions. Therefore, it is through these theories that a wide range of applications are found in thermal and fluid flows Mechanical engineering„ electromagnetic fields, bio-mathematics. Progress and an analysis of the advantages of the finite element method were made. The theoretical generalities of the numerical technique, its scope, applications and research opportunities using this technique are explained.