<p>Induction heating is an important technology for many engineering applications. Its modelling and analysis are challenging because it is a multiphysics phenomenon coupling geometrically nonlinear mechanics, electromagnetics and heat conduction. One of the challenges is buckling of thin plates and beams due to high temperatures and thermal gradients. The mechanical buckling changes the electromagnetic configuration of the model, thus changing the thermal solution, which affects mechanics back leading to a fully coupled problem. While this phenomenon has been studied numerically in the literature, it lacks an analytical treatment. We propose a closed-form analytical solution for the post-buckling deformation of induction heated beams. Using the solution, we conduct multiple parameter studies, aiming to gain a foundational understanding of the behaviour exhibited by the coupled system.</p>