The increasing interest in flexible electronics and flexible displays raises questions regarding the inherent mechanical properties of the electronic materials used. Here, the mechanical behavior of thin-film transistors used in active-matrix displays is considered. The change of electrical performance of thin-film semiconductor materials under mechanical stress is studied, including amorphous oxide semiconductors. This study comprises an experimental part, in which transistor structures are characterized under different mechanical loads, as well as a theoretical part, in which the changes in energy band structures in the presence of stress and strain are investigated. The performance of amorphous oxide semiconductors are compared to reported results on organic semiconductors and covalent semiconductors, i.e., amorphous silicon and polysilicon. In order to compare the semiconductor materials, it is required to include the influence of the other transistor layers on the strain profile. The bending limits are investigated, and shown to be due to failures in the gate dielectric and/or the contacts. Design rules are proposed to minimize strain in transistor stacks and in transistor arrays. Finally, an overview of the present and future applications of flexible thin-film transistors is given, and the suitability of the different material classes for those applications is assessed.