This paper is concerned with theory of fractal structures as well as practical implementation of them in civil engineering. In theoretical part of paper analytical and numerical analysis of simpodial fractal tree are shown. At first one, the directions of main stiffness of every point on simpodial tree are obtained as well as these stiffness. Also the ellipse of displacement of every point on tree is calculated and also a formula for center of mass. In numerical analysis, the modal frequencies are determined and the localization of modes is noticed and afterwards the ratios between modal frequencies are compared to theoretical assumption, shown earlier. At second part of the paper the design project of the airport terminal in Novi Sad whose main load bearing system are fractal pillars. Firstly, the comparative analysis of fractal pillars with different angle of branching. The whole design is done according to Eurocode, thus satisfying the criteria of limit state, serviceability and stability.