The purpose of this document is to study the application of Tensegrity principles on tensile textile constructions, which is one of points of the PhD Thesis that the author is writing under the tutorship of Prof. Josep Ignasi Llorens and Prof. Ramon Sastre, professors at the Polytechnic University of Catalunia. This work studies the basic concept of Tensegrity unit, its classification according a previous researcher (Anthony Pugh) and the author’s contribution, focused on new generations of forms. Through the geometry and computer software, another typology and a constructive simple method is developed, bearing in mind, some aspects as important as system pretension to find its balance. The objective principal is to contribute in a particular way to the application of the tensegrity in architectural spaces, in this case sports spaces through a new proposal that generates an external ring in tensegrity with a central dome, free of any interior support, by formfinding a diamond membrane pattern with discontinuous struts in a double layer that find their equilibrium through the tension of the membrane. In the following examples one can observe that traditional tensegrity tendons are replaced by membranes Fig 1, which is the main contribution of this work that finds geometry and its constructive method of the different prototypes with the help of software like AutoCAD and WinTess (a software development by Ramon Sastre), which verifies the structural equilibrium.