Design/methodology/approach A flexible gas foil bearing with a flexible arch structure is proposed, and a hydrodynamic model containing mechanical characteristics of the foil contact as well as a thermal analysis model of the bearing system is established to predict and compare the effects of the two structures on the thermal characteristics: the stresses and deformations. Findings The findings indicate that under the same load and rotational speed, the flexible arch structure bearing exhibits significantly lower maximum stress and surface displacement compared to the initial structure. In addition, the flexible arch structure shows reduced stress concentration and a more uniform stress distribution However, the surface temperature with flexible arch structure is larger than that of the initial structure under the same working conditions due to friction formed between the foils, which may lead to performance decrease. Originality/value This paper proposes a new flexible arch structure that can reduce stress concentration. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-06-2024-0225/