The purpose of research is to determine the influence character of the way the composite rope is connected to the permanent structure elements on its stress-strain state and to develop a determination method for such a state. Research methodology involves constructing the models of interaction between rigid fibers in a rope of composite design, using the methods of mechanics of layered composite materials, with complex consideration of its design and mechanical properties, and the condition of connecting rope ends to the permanent structure. The model is solved analytically using Fourier series on a discrete axis of layer numbers of a finite length while defining the distribution patterns of internal forces and displacements in rope layers. The algorithm for determining a stress-strain state of a rope with rigid fibers while considering a rope connection scheme to the permanent structure is established. The scientific novelty of research is in determination of the character and influence mechanism of a connection scheme of a composite rope with rigid fibers to the permanent structure on its stress-strain state. Practical value of the research is in that the obtained results make it possible to consider the influence character of the rope connection scheme to the permanent structure on a rope stress state and this allows justified determination of its safe operation conditions.