The finite element method (FEM) is a numerical technique for solving problems which are described by partial differential equations or can be formulated as functional minimization. A domain of interest is represented as an assembly of finite elements. Approximating functions in finite elements are determined in terms of nodal values of a physical field which is sought. A continuous physical problem is transformed into a discretized finite element problem with unknown nodal values. The key equation for solving finite element problems is {Force}=[Stiffness]{Displacement}. Dimension and values of force vector, stiffness matrix and displacement vector varies for different element types. Due to its large computational size finite element problem needs a computer program to be solved. General Finite Element Code (GFEC) is a type of a computer program that uses the finite element method to analyze a material or an object and find how applied stresses will affect the material or the design. In order to illustrate computer implementation of FEM, General Finite Element Code (GFEC) program has been developed in FORTRAN language. Different elements have been incorporated in this computer program. Out of those elements, following elements have been discussed in this manual. a) 3-node plane stress element b) 4-node plane stress element c) 4-node tetrahedral element d) Nearly incompressible 2D plane stress element e) Lumped plasticity frame element Theory and solution process for these elements have been collected from various books and journals. Collected information have been included and organized in this manual in such a way so that reading this theory manual, users of GFEC can understand the behind the scenario process.