Tensegrity rings, sometimes also called hollow ropes, tubes or sleeve modules, are systems based on straight prism geometry and composed of one or more bar circuits and cables. Recently, we developed a general study for these structures, including their ability of folding. We designed and built a human-size prototype of a pentagonal tensegrity ring with 30 cables and 15 bars, connected to 15 nodes symmetrically spread on three layers. This prototype has been tested under compression loading in several experiments. Finite element (FE) simulations are consistent with the experimental observations. In this paper, we present an analytical model of the axial behaviour of such a ring. We show the influence of each element on the mechanical behaviour of the structure, and our study can be seen as a first step in adapting the response of the system to a static or dynamic behaviour. We also provide a rheological model for its axial behaviour under compression. Our model is reduced to four springs and gives an axial mechanical behaviour identical to that obtained by FE simulations. Thus, a macro-element tensegrity ring is presented which connects the axial symmetrical load to four nodal displacements.