The disclosure relates to a flexible switch element for a track carrying rubber-tyred trains comprising two parallel rails each having an upper running surface for the tyres and an inner side surface for supporting a continuous strip (B) for guiding the train. The switch element has at least one hinge providing the longitudinal link with an adjacent switch element. The switch element also has a set of longitudinal abutments engaging, on the one hand, with the hinge in order to adjust the relative angular orientation of the element and, on the other hand, with a pivoting bottom rod providing the connection to and the alignment with an identical switch element arranged symmetrically on the opposite side of the switch. The disclosure also relates to a track switchgear comprising the assembly of such elements and a method for transporting passengers along a track provided with said track switchgear.