The methods and algorithms of generative modelling can be improved when representing organic structures by the study of computational models of natural processes and their application to architectural design. In this paper, we present a study of the generation of branching structures and their application to the development of façade support systems. We investigate two types of branching structures, a recursive bifurcation model and an axial tree based L-system for the generation of façades. The aim of the paper is to capture not only the form but also the underlying principles of biomimicry found in branching. This is then tested, by their application to develop experimental façade support systems. The developed algorithms implement parametric variations for façade generation based on natural tree-like branching. The benefits of such a model are: ease of structural optimization, variations of support and digital fabrication of façade components.