The thesis presents a method that can be used to create plant models that can be displayed efficiently and directly on the graphics card via a finite set of elements and a set of rules that define the matching possibilities of the elements. The need arises because alternate methods for displaying similar geometries are often computationally expensive and do not allow real-time animation of the models. The solution supports the skeletal animation of the models, whereby the same topology plant models, created with the same rules, will pick up a unique pose. Also, animations can be implemented that simulate motions generated by wind. The created models are different, so they do not have the effect of showing the same model several times. I made the models of the finite set with a modeling program. To increase the efficiency of displaying on a computer, the models can be displayed at different levels of detail. The production of models at different levels of detail is ensured by hardware tessellation. Thus, when approaching the plant models in the application, the models will be displayed with a higher level of detail. While far away from the models the level of detail is low, because the displayed models are the non-tessellated original versions of the models. My implementation allows easily expansion of the element set and element connection rules.