Deformable cell model is developed to study pattern formation and to simulate plant tissue growth. Each cell represents a polygon with a number of vertices connected by springs. Some cells in the tissue can grow and divide, other cells are differentiated and do not grow or divide but remain deformable. The model is used to investigate formation of self-similar structures which reproduce the same cell organization during their growth. In numerical experiments we observed that self-similar solutions can exist for a rather precise choice of plant structure and mechanical properties of cell walls. We test the model for simulation of apical meristems functioning which represent self-similar cell structures in plants. At the next stage of modelling, auxin distribution is introduced by means of diffusion and polar transport mechanisms. The existence of steady auxin distribution in a growing root is investigated. Single as well as multiple auxin maxima have been observed in model solutions.