In the last few years, Additive Manufacturing has enabled the production of complex-shape components. Among them, TPMS represent interesting geometries being easily 3d printed without many limitations. TPMS represent a fascinating family of metamaterials that are mathematically described through a trigonometric equation in the space R3. TPMS structures have no sharp edges and corners, and split the space into two non-intersecting domains. Among the available TPMS, we focus on the gyroid. Herein, we first generate elongated gyroid-based structures obtained with the repetition of multiple gyroid cells along one direction. Then, we study the mechanical in-plane response, comprising possible instability phenomena, of such structures, exploring the effects induced by the gyroid thickness and the number of cell repetition. Finally, we develop a simplified equivalent beam model able to represent the planar behaviour of such elongated gyroid structures. As an interesting application of previous models, we propose and investigate gyroid-based airless tires. Our findings indicate that both the stiffness of the considered material and the number of the gyroid-based spokes are crucial parameters that significantly influence the performance of airless tires, in terms for example of contact patch extension and contact pressure profile.