Tensegrity systems are composed of high strength to weight mechanisms. They achieve this strength by replacing heavy elements in tension with lightweight cables. This property has led to the application of tensegrity theory to many holds, ranging from architecture to robotics. The greatest difficulty for those wishing to exploit the benefit of tensegrity systems, is the unintuitive way in which the subelements of a tensegrity are connected to form a stable configuration. In this thesis, a new method for determining these stable configurations is developed, thereby providing a more intuitive tool for designing tensegrity systems. This novel approach is called the geometric intersection method, and is based on determining the common intersection point between three constraint surfaces, each of which represent one of the element lengths in the tensegrity system. The geometric intersection method was found to be algebraically equivalent to an established form finding method by deriving the established method from the geometric intersection method. This result was further reinforced by evaluating the two methods using several different tensegrity systems. While the two methods are algebraically equivalent, the geometric intersection method is derived using geometry instead of vector analysis. This difference arguably makes the geometric intersection method more intuitive, because it provides a visual rationale for how the element lengths affect the final configuration of the tensegrity system, and when the combination of these parameters will result in a configuration that has no real physical significance. It was also found that the geometric intersection method is easier to adapt to new tensegrity configurations than either of the most closely related form finding methods.