Abstract: In this paper, the finite element method was applied togeometric stability analysis of three-dimensional skeletal structures.Two types of element geometric constraint matrices were derived. Afterassembling element matrices to form the corresponding global matrix andemposing the required displacement constraints, the geometricstability of a system can be analyzed by comparing the order and rankof the global geometric matrix. The method is found to be simple inconcept, easy in implementation on a computer and complete in itscomputed results. For example, for geometrically stable systems, the number ofredundant constraints is easily available, and for geometricallyunstable system, the number of degrees of freedom (DOF) of the systemand the corresponding displacement modes can also easily be calculated.