Composite materials are being widely used nowadays in various engineering structures including airplanes, unmanned aerial vehicles (known as drones), automobiles, sports equipment, bridges, and structures. Their vast applications in different industries are due to their high specific stiffness and strength, high production rate, ease of fabricating complex shapes, long lifespan, and so on. In this regard, employing textile composites in which the reinforcement part is a textile preform is on the rise in diverse industries, especially in the aerospace industry. So, the majority of researchers in aerospace companies, like NASA and Boeing, are interested in composite materials based on textile composites. Textile preforms are divided into two groups: two-dimensional and three-dimensional, according to the final structure of fibers or yarns in the textile preforms. Among the various textile preforms including woven, knitted, braided and stitched ones, the braiding process, due to its high capability of formability, can efficiently fabricate preforms with complex shapes; this can occur in such a way that post-processes like cutting, stitching parts, and manually placing fiber in different directions are not required anymore. Thus, the production cost and time are reduced. In this study, two-dimensional biaxially and triaxially braided preforms produced by the circular braiding machine were employed in order to integrally fabricate the wings of unmanned aerial vehicle. For this purpose, the spatial orientation of the braided yarns on a mandrel with constant arbitrary cross-section had to be investigated initially through the circular braiding process. In this regard, two theories were offered in this research to determine the braid angle. Accordingly, to verify the proposed theories, mandrels with circular, elliptical and egg-shaped cross-sections were chosen and braided. Then, the braid angles were measured using the image processing techniques on the mandrels’ surface and compared with the theoretical values. Therefore, the first aim of this research was choosing an appropriate theory to determine the braid angle on the mandrels with the constant arbitrary cross-sections. Furthermore, in order to simulate the two-dimensional biaxially and triaxially braided composites with circular, elliptical and egg-shaped cross-sections in the ABAQUS software, the governing equations in the geometrical modeling of a repeated unit cell and the effective stiffness matrix of the two-dimensional biaxially and triaxially braided composites were derived and employed in finite element modeling as the VUMAT subroutine. Based on the results obtained from the finite element modeling and the experimental tests (four-point bending), it could be concluded that the new theoretical and geometrical relations obtained in this research were of high accuracy and could be, therefore, used in analyzing, simulating and fabricating various braided composite parts with the constant arbitrary cross-sections. Finally, in order to employ the relations in real-time applications, the proposed theoretical and geometrical relations were used in simulating biaxially and triaxially braided composites with the NACA 23018 airfoil cross-section. Then, the finite element modelling results were compared with the experimental ones, achieving a good agreement.