Abstract The concept of substructuring is used to derive an algorithm of stiffness matrix inversion. Accordingly, the structure is decomposed into a set of basic structural (or finite) elements. The sequence of gradually complicated substructures is formed out of the set of basic elements. The algorithm of recursive relations between the block entries of two consecutive inverse submatrices corresponding to two consecutive substructures is derived. Two-node and multi-node structural elements are considered. It is shown how a multi-node element can be coupled with a substructure in a node-by-node fashion. A node is considered to be a rigid-elastic-hinged coupling. Two numerical examples are given, and some computational features of the algorithm are discussed.