Timber constructions are often based on simple geometrical shaped elements in terms of their cross-section and longitudinal form. During production, curved or forked components of the tree crown remain unused. Building botany has evolved as a new discipline of living construction design in modern architecture, for which trees are artificially led in the right shape. The goal is to use naturally shaped components as load-bearing members in structures. Because of the irregular geometries, it is crucial to transfer these into the calculation model accurately. This contribution presents a numerical method for analyzing the mechanical behaviour of naturally shaped timber. This method employs a generalised approach of the scaled boundary isogeometric analysis method, a technique combining the advantages of scaled boundary methods and isogeometric analysis, combined with an image-based modelling technique. Classical scaled boundary methods apply hollow geometries directly by projecting the boundary surface in a scaling centre. Applied on long and slender structures like naturally shaped timber elements, obtuse-angled polyhedrons occur within a patch, leading to numerical condition problems. The generalised scaled boundary isogeometric analysis (GSBIGA) approach avoids these disadvantages by scaling the surface on a centre line and circumvents the need for star-convex geometries in longitudinal direction [1]. The underlying material model is based on a fibre-matrix approach from [2] transferred in the realm of computational growth. The underlying growth mechanisms are based on a biomechanics method for modelling soft tissues [3]. Here, the deformation gradient is split multiplicatively into an elastic and a growth component. Specific basic growth mechanisms apply to tissues and wood, such as shape adaption and remodelling. Therefore, a formulation for modelling volumetric growth is combined with the introduced GSBIGA approach. This combination allows the modelling of the growth of arbitrarily shaped geometries, such as naturally shaped timber or tissues, based on 3D-image data.