en Structure-Steel Structure-Steel Research Paper Research Paper Formation of a suitable null basis is the main problem of finite elements analysis via force method. For an optimal analysis, the selected null basis matrices should be sparse and banded corresponding to sparse, banded and well-conditioned flexibility matrices. In this paper, an efficient method is developed for the formation of the null bases of finite element models (FEMs) consisting of tetrahedron elements, corresponding to highly sparse and banded flexibility matrices. This is achieved by associating special graphs with the FEM and selecting appropriate subgraphs and forming the self-equilibrating systems (SESs) on these subgraphs. Two examples are presented to illustrate the simplicity and effectiveness of the presented graph-algebraic method. hree dimensional elements, Tetrahedron elements, Higher order elements, Finite element method, Force method, Null basis matrix, Flexibility matrix, Graph Theory. 249 269 http://ijce.iust.ac.ir/browse.php?a_code=A-10-218-68&slc_lang=en&sid=1 A. Kaveh alikaveh@iust.ac.ir 180031947532846008029 180031947532846008029 Yes Iran University of Science and Technology M.S. Massoudi 180031947532846008030 180031947532846008030 No Iran University of Science and Technology