The present paper deals with the theoretical and technical reflection on basic structural principles that allow the generation and controlling of architectural complexity of double curvature surfaces.Despite the difficulties in designing and building such complex forms, Chile has several examples that were developed and built during the first half of the twentieth century. All of them were developed with local building technologies which studied the implementation of experimental and simple materials with innovative mounting techniques. All of them explored new structural concepts generating great interest of architectural spaces for religious cult, housing and civil works. The research objective of this work deals with the recognition and analysis with contemporary modelling and simulation tools that can reveal the type of relationship that occurs between the initial conception of the architectural shape and membranous structural surfaces. Their curvature and sleekness generated innovative structural spaces that contain an architectural envelope with clear and revealing expression of the acting forces.