It is pointed out in this paper that there exist some improper statements on the rule of the nodes of a natural mode?shape in monographs, textbooks and engineering manuals related to linear vibrations. Hence, detailed discussions are made on the theorem of Гантмахер and Крейн about the natural mode?shapes and their nodes, as well as their preconditions in order to call attention from both academia and industries. Afterwards, a complete analysis is made for the node number of the natural mode?shapes of a two degrees of freedom arbitrary linear system. Based on the analysis, the natural mode?shapes of a kind of multiple degrees of freedom composite systems are studied so as to demonstrate a designable relation between the order of a natural mode?shape and the number of its nodes.