Abstract: The theorem of structural continual variation is applied to the analysis of the reliability of plane truss structures. On the basis of the branch-bound method, a computing program is developed. The repeated assemblies of the global stiffness matrix and the repeated inverse operations of the matrix caused by uninterrupted changes of structure topology can be avoided. A new criterion for degeneration of structure into a mechanism is introduced. Both the sequential analysis for the structure continual variation and the generation of the limit state functions of structure can be realized. Moreover, the generation of the probable failure chain and the calculation of the failure probability may be simultaneously accomplished. In the searching the probable failure chain is efficiently selected and the set of the probable failure models is also given. Therefore, the theorem and the method indicated in this paper is useful to solve some practical engineering problems. The results of the calculating example are satisfactory.