This paper presents a novel approach for analyzing plane frame systems by using Finite Element Method. The topology matrices are used to analyze the system. The releases may be easily assigned to elements and any boundary conditions may be applied to the system. In analysis process, all frame elements are assumed as having rigid connections, even though elements have releases or not. Additional freedoms are added to the nodes to consider releases. The coordinate system of nodes can be changed and supports can be assigned with any angle. Additional freedoms and the coordinate system rotations of nodes are taken into account by using topology matrices. An educational program was developed to analyze frame systems by using proposed approach. A numerical example is taken into account to explain the analysis process. The results of numerical example have compared with SAP2000 structural analysis program and suitable results are obtained.