This paper presents the synthesis of multiband frequency selective surfaces (FSSs) using supervised machine learning (ML) with the decision tree (DT) algorithm. The proposed FSS structure is composed of an array of metallic patches printed on a dielectric substrate for stopband spatial filtering microwave applications. The shapes of the metallic patches are based on the sunflower (helianthus annus) geometry. In the first step, a parametric analysis is performed to investigate the use of different FSS geometries, including those with circular, annular and corolla integrated patch elements, to compose the sunflower geometry, regarding multiband and polarization independent performances with size reduction. Two bioinspired FSS geometries are synthesized using supervised machine learning with the decision tree algorithm. The random forest (RF) algorithm is used to validate the decision tree algorithm and to confirm the obtained results. The numerical analysis of the proposed FSS geometries is performed using Ansoft Designer software. Prototypes are fabricated and measured. The good agreement observed between simulated and measured results has validated the proposed approach. The use of supervised machine learning with the decision tree algorithm resulted in a particularly efficient and accurate synthesis procedure due to its intuitive implementation and simplified and effective data analysis modelling.