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In this paper two types of finite strips for modelling vibrations of a rotating tyre are formulated: a cylindrical and a toroidal. Cylindrical strips are used to model vibrations of the tyre belt, whereas toroidal strips are used to model vibrations of the tyre sidewall. Both strips have the advantage of exactly describing how vibrations depend on the circumferential coordinate. Hence, only a cross-sectional discretization is required which significantly reduces the computational effort. Furthermore, either strip is a sophisticated finite element which is able to capture special effects due to rotation and pressurization of the tyre. These effects include the hoop stress due to the pressurization and centrifugal forces and the corresponding upward shifts of the natural frequencies. Additionally, the two strips can model Coriolis frequency veering and the corresponding rotating vibration modes. The new finite strips are validated by comparisons with analytical results and full FEM discretization for basic geometries, a cylindrical shell and a torus. Excellent agreement of the results is observed for stationary, pressurized and rotating structures.